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# Work: https://leibnizlegible.com/work/782001750
# Title: Exercitatio Geometrica (shelfmarks Leibn. Marg. 37, Stück 1; Leibn. Marg. 37)
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=782001750
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a
se
L
3
i
X
c0
D
A e
e
u
Mitrotilm- System-Vertriet

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ib. Mra
 ire

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e
Leibn. Marg. 37: L eitn. Mar9. 37, 5

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Vat: Theum
vhito
aoia

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2
eatl LLLLLC
+
AALLALLLL.
De Creometria Indivisibili
um, et Proportione Spiralis
ad Circutum.
AuthOTE, TIOMA ANOLO,
ex AL. BIIS Fast- Saxoum.
nar
o
n
LONDINL.
b 0 adloc

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i
C
si
dton.
7
podnetarum
.

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ed ex
es
asoc
ae
 (d  ((A E). 2)D c
e dio di c
d
b
ad
ol
d
Fxcelsentissimo Viro,
0
ierardo Cmsovoron:
n
in Medicina experienei
simo, in Creomecticis Thau-
maturgo, de Mathemacum
apud CTRVDTOS. PFO-
7
EcsOrL RECoIO.
Vboluerat PTIYSTCO meo
ETCL. IDI (Clarissime V ir
defensio CARIESII, guam
e
moliris. Inhorruit;  exclamons,
Periimus, inquit In procinetu act-
versus nos stat, Carretuhyperas
istes, magnus CTATSCEIL
A3
VES

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VEK. Frcgo, ab amicissimo viro
Ouidrimes: Ne naevos tibi tuos
aperiate iabebate Venes suos;
ns
macis. Plura ad solatium addidi,
o Fratris MIETAPTITOIES
auxilia spopondi. Surdo canebam:
Rotulit mibi. Oud haec ad tancum
virum, Cicomeeria callentissi-
mum. Idacura per medicas inda-
rationes Lvisceratorem, qui per
Mechanices operas, vitam, imo
qa
Mencem, antomatis indit, ut peri-
cula zitent, ad tutarecurrant, Cx
Cartetio, (Ouanto Philosopho.)
1.
unclis viribus campum invacit s
Sede mul, inquit, domi expro-
bratur, Onde rn Demonstracor.
um CICOMCECICA non attigeris
Pu

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Putasne posse leges  Solertiam
Cicometricam ad Labyrenthos
Patura, es sepositos SaPICHEIZ
recessus traducere: AB laterl
tlac dicipotuisse, e non potu
ille retelli e
Agnovi voces debentis Fridano
hustuarium. ex nefastum erat omen.
Colleei itaqne metorum, e cuni
hane FXercuationem pariuriis
sem, ECICLIBI minori ad te
perferendam tradidi, ut palpo te
feriat.  Fracri moltes exoret
iras: non ui parcas ipsus vitus
Caegnum enim est ut sit amicior ve
ritas): sed ut doceas, non confui-
A3
das

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das erndias, non exaertes; me
Tuo. admiratorem maris indies
reddas
n    L A. X d. L l lt L d A 9
lda  L L11
d
e

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ATIC
 n  L 9 C
L  a n  i
EHcercitudo _. vaniras, quae jam an-
ce saeculum Scholas MeraphyliCaS,
e iplam Nacurae discustionem (ubi
Medicorum industria non lesemilcu
ic) invalir ee pessundedit, cantanau-
sex tuic Machemarum consultis, uc
erirari cuiliber ab ipsarum Foncibus
derivatae eo ipso siugaciratis ee lo-
philmatis macula apudeos (Catero-
quiacucissimos d lolidissunae censurae
caereras hranc calumniam duae adnar
c
sibi ce amaono Aristotele demonstra.
es
ea sententice: Paries videlicet non esse
actuin continuo ) marno, e Non esse
resolubilem magnitudinem in indivisibi-
lia. Ex quarum ionoratione radices
Tubnisix celebris illa, apudModernos
incauciores, Demonstrarionum balS:
uaM
t

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 LL RCIC A 1
Quantum non esse aliu d quam sua In d
vesibilia. Duxe quam lare le expanderic
vixestdicere, maxime ex quo ingeni
olissimus C avallerius, quali novam
icienciam orditurus, eometriam
Juam (quam indivisibilium apclla
VIC) publico erpoluie. Memini incer
venisse dum librum luum praelo non-
2
dum lubaccum sidissimo Cralilaei dis-
cipuilo D. Benedicto de Castellis obtulit.
tanei visi auchoriratem exambiens:
qui post dilcectum Ruclioris de OpCrC
cum non levi stupore locurus, maceri-
ei univerlalitarem e merhodi clari-
iacem mihi aperuir. Neque inficior
me, e dicentis veneratione, quempro
lummae ingenuicatis e lcientix viro
merito colebam, _ ingeneis ausilpe-
C
ctabilisima facie actonirum, miro
publicacionem operis expectarisse at-
tectu. Sed cum cenacior torem corum
doematum quae ab dristotele eED.
Thoma Aquinate proAxis acceperam,
methodus Cavallerunon ciera formi-
dinem mihiinsedie, quae medicarione
mulis adeo invaluit; ur iplam me-
thodum

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GEOME LRTC A.
ahodum, CrInOn DenituS alperMAn=
dam vel inurilem, camen tallacem de
non sine examine adhibendam incel-
lixerem. Lc quoniam eam minium
avide desluriri a Geomerris coresiis
adverterem, cur mibii displiceree in
paculum propellere, operee precium
vilum elt. Aiopronde dictum hOC.
Quantum esse omnia sua incivisibilia, in
Schola Cheomerrica elle eHaru e ac-
cepratione indignum. Quod uc ipsius
scientiae propruis celis conticiam, me-
mororrium generum esse indivilibi
lia, quae truic dispuracioni submirtun
turz Puncta, quasi clemenra lincarums
Lineas, Cuperticierum partes, _ Super-
ficies eandem ur in corpus aediticatas.
In lingulis aECoMETe lV venaMUT.
Geomeum Indivisibilium esse fallacemo
Ccurrunt Ctarim nocissimae leges
Diamerri e coltx in quadrato.
Cumenim nullum sic Punctum dia-
merriper quod non eranteat lincare-
cta ab una duadrari cosed ad oppoli-
Ea n

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 DM
 AL seb
taque
tam parallele adbales acta, fatuum
L
ele espectare plura puncta in Diame
e
quc
troguam in coltas d lammen, diame
a
crum negare colta lonsiorem, neque
po
Geometria permutir, neque ocuI.
5
Neque minus nocum eltncquemi-
nus clarum quod lequituri nempe pol
seCurvas intinicas ejuldem esle altitu-
c
dinis, len eidem axi applicari, qua
rum alia aliâ sic longior, et lincula
longiores axc; e ramen a lingulis
punctis curvarum ad axem duci po-
oc
He lingulas lineas parallelas sibi in
c
vicem, utnon plura necesse suc in Pin-
quc
rulis curvis ese puncia quam in aXC,
hocele, ur su punctorum in longitu.
dine inaequali mulceudo lemper
aequalis.
Ouortum adjiciam, Ci ex CeHETO
eue
advalcimumae Circumterenlla lingula
puncta lincula linea per lingula iccm
c
puncta concentrilarum circumteren
riarum deduci natae sine, aequa mul-
titudine punctorum omnes Circumte
Ferencias conslari, nihil impedience
quancaliber donsicudinum varietare:
DUOE-

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EXEROITATIO
Ouorlum, decimam lexri Plemen.
Cd. s
rorum in quanculacunque rella, par-
res quanexcunque parribus mulcitu-
dine aeguatas, cum contensu ipsius ce
ometriae invenisle ?
Nonminor est in cateris indivili-
bilium speciebus copia. Inter casdem
Parallelas, si Cacuatur unum paralle-
logrammum cujus lacera sint perpen-
dicularia basibus, licebie Formare alia
quorlibet inter ealdem parallelas lu-
per equales bales, quorum lincula
lineae ad lineasprioris sint inquali-
cunque proportione, d omnia paral
lelogramma nihilominus spariis aequis
FInIenEuI.
s
Suxer diamerro quadrari consistane
quaelibet portiones circulorum vel
aliarum tixurarum cueri lincarums
quorum currae, lincas quodrari pa-
rallelasbalibus, in binas partes inx-
qut
quales secents parreslinearum paralle-
larum balibus in quadraro per quam-
et
liber divisionem tacla, erunt aequales
libi invicem e longicudine e mul-
cicudine; cum inrer omnes una une
lempet

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_XFRCTTATIC
Temper reperiri pessit aequalis, cum
alcdtigurarum per divitionemm naca
rum pottine eAe in quancalibee, IMa
qualicate.
Eadem lege, in quibustibce Aouris
Planis conrinue in vercicem deticienci-
ous, modo linebalium aequalium, re
Peribiles lune lingula lineae lingulis
e
aequales cum inaequalicare arcarum ad
libicum.
Figurae dictx Tloperimerra a Tri-
ansuloulque ad circulum habent lI
neas quibus constant a cucumteren
ciaulque ad centrum analoge lurrip-
cas lemper aequales, cum arex polline
quantamliber variecaren terre.
Superlune superticies non minus
terciles. In corporibus similibus sed
inaequalibus, ABUrR IMTCOEaNTeS COF
puslune lingulx acque adeo omnes IM
Supla proporrione lacerum Homolo-
Gorum, led corpora in exipIa LaTIOHC
corundem.
Coni aequalium alcirudinum e ba-
sium cum Cylindris, constane ex co-
nicis superticiebus Factentibus medi-
etatem

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GFOMETRLCA.
Ctatem spacu quam faciunt cytindri-
caesuperticies cxlindrorum, X camen
cons tune cercia duntaxat pars cylin-
drorum.
In ficuris Tolidis basium aequalium
continue ad verricem deticienribus
Parallele ad balim, non elreperire
superticiem bali parallelam cui non
reperiarur alia in aliis aequalis, ets
ipla corpora sinc civersssimarum mo-
HIum.
Hlemisphaerium ex superticiebus
hemisphaericisconstare, indectrina ce-
ometrie indivilibilium, contellum elt.
Idemhemilpharium ex planis circulo
maximo parallelis, quorum sinoula
siur aequalia sinculis balibus superti-
cierum hemilpharicarum non minus
dilucer, e hoc quidem in alcitudine
axishemilptiaeru. Superticies autem
hemisphaericas esse duplas suarum ba.
Tum, non pacitur dubicaie Archimedes.
Duare, liper indirisibilium compu-
cum quanciras hiemilphaerii aeltime
tur, pronuncianda elt esse sibimet
dupla ec dimidia.
ctoe

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GF OMF TRICA.
Hlaec acervatim congessiline figuris
 deductione, velur nora Cieomerris
ad quos mitui res elt. Neque finis
exemplorum Forec h liberer prolequi.
eniverlam liquidem Creometriam
convellir e everrir haec Fallax me-
thodus arguendi.
Fundamenta ipsius esse debilia.
7
Erum enimvero audiendi TUNE
velerroris patroni, ut riecon-
demnentur. Allesant itaque ipFI
is Instantias plurimas, in quibus haec
ous
methodus veritarem terioir. Scd, Pacc
tantorum virorum dictum sit, neque
Cicometriam neque. Losicam Lapie
haec argumentario; postquam et L.o
ca docer centum exemplorum my-
riadas regulam univertalem non lan-
cire, s vel una sc in oppolitum clara
instantia; d non lic e Geomerrarum
dilciplina ab exemplis, sed a definici.
onibus ex de se noris Ariomatibus, Ar
mitatem petere.
Replicam, ex acure; Se posle cales
limi-

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P XEROITATIO
limirationes principio assumpto ad
junsere; ut non possit Fallere hic dil
currendi modus. Sed in primis ex-
pectanda eshaec opera. Verumpres
hus urgeo, Num addicis hislimitatio
nibus, ex cerminis clara erit propoli
tio, se sua Ccabilirare constans: An
ideo accepranda, quianondum appa
ruic in deducrionibus lapsus: Si hoc
posterius volunt, interca incertOS 
ienorantes nos relinquune. Si PriuSs
Ulc quid hanc evidentiam non pro-
mune, uc acquielcamuse Sed hoc non
n
Polle heri non iplorum duntaraerar-
dicas e mora convincit, led quodcer
a demonstrarione phytica consternul-
a omnino esse indivilibilia in magni.
cudine, e proinde vanissimam esse
propolitionem, quae cam ex indivilibi
libous CompOnIE.
Unde irrira evanelcit calumnia illa
quam iaccabant e anriqui SCcPECI
e quidam moderni (quod puden-
dum est) non leviter Ceometricisim
buci; Videlicer Cieometras, vel macis
iplam Ceomerriam, falla quaedam
uppon

## Folio  -  — 782001750:0020
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EXPRCILATIC
supponere, in quibus tunder, quae cer
ea reddere pollicetur, utiquenaec ip-
Ta indivilibilia de quibus est fCrmO.
Credune siquidem Ccomerras, cum
e
puncca de lincas, ec plana delionant;
reaple exiltimare quaedam entia indi-
vilibilia in iplocontinui concextuna
rere, ad quae corum delionacio ter.
mineiur, ionorances his voculis pu-
ras neoationes explicari, uc supertici
es, quatenus indivisibilicatem lonai,
non lic aliud quam non-profunditas, li
nea, non-latirudo; punctum, non-longr
tudo. Cum icaque allerune vel luppo:
nunc Creomcer
punctum, non aliud volune quam lon-
gicudinem non ultra prooredi; cum
lineam, lacicudinem esse Ainitam; e
per Luperkiciem, quam nOMIMaNE PTO
Fundirarem Peu corpus, vel corporis
eam de qua Loquuntur parrem, nOn
lemet ulcerius exporrisere indicant.
Maleiraque intellisune Sccprici; non
12
Sed replicane Sceprices cultores:
Demonerandis GEOETIL
CIEIS

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GFOMETRTOA.
ciris non heri lacis, nis incelligatur
duciposse lineam a puncto ad punctum
quando id postulant, vel planum adi-
si posse per corpus qua iplijubent, de
propterea incroduci ab ipsis quaedam
rracis concedenda; a secusnitiil pol-
leCeomceriam. Neque licer inficias
ire quaedam a Geomeeris poltulario
Sed ii ulera corticem inlpicientes
quaeramus quaenam Aasicentur, inve
niemus nil aliud peci nsue dilcens,
scu lector, velic animum sc applicare
ut a Maxistro ducitur. Viccenim hu-
jusdicti, ducatur linea a puncto R. ad
punctum B. Cubjiciatur tiaec proxolicios
Abstrahendo a latitudine, confidera (olam
longitudinem inter A.  B. Lancun-
dem dictum erit, et tictionis indivili
bilis Fincicacis nullum apparebit ve-
Aisium. Simile cR, l pro Transeat pla-
num doctor edicae, apprehende latitu-
dinem in parre quam ostendo, obstrahen.
do a prosuxditare, Icu non considerata pro-
funditate. Fodem partu proorediernt
demonstracio, e luspicio de adjeci
ELd

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EXEROITATIO
tia supertcienulla supererii. Palam
elt iraque Ccometris non cse necet
lariam aliguam efectionem ad postu-
laca lua, led vice abstractiorum MC-
captivlicarum, ad incellectus sis non
aluetactos formulas iudiores sed ac-
commonatiores adlibere.
Riguis incommoda ad lndivisibili-
um policionem Lequentia Vicaturi, Pro
lincis parallelosramma, pro (UPer-
ficiebus cylindrellos vel parallelcpi-
pedamiuma lcu renvissima, uc itifi
Fita Cractane, lubornane, ICIP. a VOCCS
non rem mutantes. Incer liujulmodi
enimquantitates, vel aliquas cse mi-
mimas pucanevelnulla. Segux mini.
e
Line e ulciudo intinita, palam
 quancitares ex IIS compotiras cAe
anicudines intinitas, quoc lorum
Geomerrarum propotilo non conre-
nit. Sin aue mulcicudinem horum
cerancoru simcam, acieniulla mmini
acredaues corpora quidem Anita,
led ad praelumpeas plorum demon-
Era

## Folio  -  — 782001750:0023
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GFOMF TRIOA.
strationes nihilo magis conterentia
afterune. Vereenim sinullae tune mi
nit e LIAFUM QUANCITATUE, OMIMES NOM
Cunc nisi pura indivisibilia.
Depuonane adhuc, de Creometra
rum insignium quihiane dilcurtusra-
tionem amplexi lune auchoricace; e
C
Lacilicare ad inventionem quani cx-
perti lunc in ca summano Ad pFOA
centes se nominum ajestatem reve-
reri lic opponitur. Videre, num deceae
Maristros in Ceometria ad authori:
carem appellare. Ouid quod ienolci-
bilius uir invento proprio deceprum
elc quam in alienum errorem ele do-
milisse: Turpis itaque Ccomerrae cAt
haec exculatios
Deucilicate ad problematum eno-
darionem respondendum est, Ilane
commodiratem Dialectico dilpucato
imire congruere, Demonltratore qui
pie
leveritarem ambiat, esse interiorem
Bar

## Folio  -  — 782001750:0024
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 26 lines, status machine
B AEROIT ATIC
am ad antiquam methodum factiss
traduet.
darum est errorem octendisse;
maonum ei ucilitarem quae ex ip-
ius admissione sperabatur ex alio ca-
pite doceas acquirere. FR itaque
quam lperane ucilicas, invencionis
et
Facilitas. Flaec, quomodo xqualisha-
veri porte in mechodo corporum, ab-
que periculo illo erroris quod lecum
cratuie indirilibilium policio, nobis
ostendendum manee
Modus icaque perquanta, demon-
Eraciones conjsacas 1IS Qua per me-
ehodum indivilibilium prxcenduntur,
Anpendi, a cribus propoucionibus pen
der. Prima elt, Demonstratio seu effe-
etio, quae excludri omnem differentiam quae
possit oljiei, probat aequalitarem. Ilanc
Tola terminorum apprchentio tacire.
videncem. Si enim duo difterant, cerra
ee determinara quancirare difterune,
quae l objiciatur non porest excludi à
qua

## Folio  -  — 782001750:0025
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
GEOMETRTCA.
qualibee demonstratione. Si itaque
demonstracio excludar quamlibet.
hoc eAtnullam non excludae, clarum
eArullam omnino cse.
Proxima propolicio eA. Cuilibet
quanto a bast ad rerticem continue defi-
cienti conseribi posse sive intus sive extra
ver bidivisionem seu dichotomiam axit 5 (9
partium ejus; es ordinatim factas lineas
vel plana parallela best alia quanta qu’ae
differant a dicto quanto quantare minori
qualibet oblata.
F. L. JEAOitaque A. B. C. quantum d
hallad verricem concinve deticiens, cu-
jus axis AC. divilus scbitariam in D.
dE parces AD, DC. ierum bitariam
divilae in E _C F. _ imperacum lc cir-
caquancum ABC. conscribere aliud
quantum non excedens Quaneum
ABC. Mole quanciratis dabilis, _ lit
quancum oblacum o. Incellisatue
vero eAc planum, ee quancicas
ABC. Smilicer plana, et hac parai
x
deloorammum reclangulum luver re
Cda
d AP. aequole aXI AC: minuS (pa-
E

## Folio  -  — 782001750:0026
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
a 
i
PX LRCElATIO
cio 0. Sique reliquum latus paralle
logrammi, IR. _ hac AL perpendi-
ta que
cularis AXI AC. aqualis reclae lH.
e excirara perpendiculari a puncto
L. ad lacus quanti propolu L M.
mulciplicentur divisiones AXIs donec
singulae parces sine breviores linea
L M. Se ductis a divilionibus axis li-
neis parallelis bal (quales TUnEE N.
OP. aF.) excIrentur a punctis N P.
5)
perpendiculares aequales parribus AX-
i5, e productis parallelis perticiatur
tioura ex parallelogrammis qualia
TUNEBF. Q D. PF. EE NA.
Fc dico quantum consistens simili-
bus parallelogrammis Factis excedere
quantum ABC. MIHOTI QUanTITaTe
quam sc assienata c. Cum enim pa-
ralleloorammum E X. sic minus
quancirare 0. e parallelogrammum
ex omnibus partious aXis in. P A. lIC
xequale parallelogrammo IIK. e pa-
ralleloorammum I MI a. majus Pa-
calleloorammo quolibet ex una parre
arisminori linea L M. In PaFTeM rC-
Eta

## Folio  -  — 782001750:0027
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
GEOMETRICA.
Atae Parallelae bali quae Cst exera quan-
tum ABC. Q inceerar lacus paralle
loerammi ex inccora linca In PATTENL
axIS minorem quai liCL. MI. DaFaI-
leloorammum ex L. MajuS CriE OIM
nibus parcibus fioura ex parallelon
ZTaIIS Que TUNE eXETA QuUaHTUI
ABC. X Per ConsequenS FigurA CX Pid-
rallelogrammis excedir quantum 
BC. MInOTI QuaNCITAEO Quam LIC O.
Quod eracprobandum.
Sicur de planis Drocessimue, de cOr
Poribus cacem mcctiodo Ac proores
lus; Ouare univerlalicer demonltrat
eltpropoluio aNumpra.
ultoitaque terria propolicic: Duc-
quid praetenditur demonstrari per propor-
tionem indirisit ilium per moihodum pro-
posiam, aequan Facilicate demos. rATE. Y.a
tum est ex 2LhujuS Methoci, 15 ab eaba-
bet firmitarem.
Cum enim incivisibilia non posine
comparari ad leinvicem nIlLHUMIEIO
magnirucline, d provorcione, leu Oin
dine, clarum quoque suc muicirucIS
B 4
CO13

## Folio  -  — 782001750:0028
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
PXEROTTATIO
comparationem nudam vanam eAe
cum in omni quanto line intinita.
na
Icem comparationem marnicudinis
nullam esfe posle nili numeri racioha-
beacur, cum plures minores Faclane
aequale paucioribus majoribus, hede
A2
polle cum apparentia renrari nili per
ordinem seu proportionem quae repe
riri polsi incer indivisibilia; sive in-
divilibilia ejuldem corporis compa-
rentur mucuo, live indivisibiliaunius
quanci ad indivisibilia alceriu:-
Duare cum necesse sic posse Fabri-
cari quanta luper indivilibilia in ca-
demproporrione quam habent indi-
vilibilia, planum est per ipla quanta
parcialia (uc in merhroco tactum cA)
posie aroumentarionem construi ae
quali facilirate arque per indivilibi-
lia, imo reipsâ esle ltructam EI dun-
TAXAE MUITeHEUE VOCeS X vice hujus
Ind visibile A. est ad indivisibile B. di-
CaTUIT, Cuantum cujus basis a est ad
quantum cujus besi SD.
C

## Folio  -  — 782001750:0029
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
GEOMEVRIIC A.
F. 2.) FCto enim (exempli causd) in-
centum Creometrae probare aequaliracem
circuli cum Triansulos cujus lacerum
circa ansulum rectum alrerum aequa-
de sic lemidiamerro, alcerum circum.
terentia circuli, quod est primum ex-
emplorum quo Torricellius. Cicome
cra elegancistumus, contirmar doctri
nam indivilibilium licelto Agura,
quam ipse proponit, Triangulorum
ABC. _ AIL. SC circulorum DB. e
OT. Arsuirille, exaequalicare perio
pheria OT. ad lacus IL. hoc ett, Cin-
sularum peripheriarum concenerice
inclularum in peripheria DB. ad (in-
CL
aleraes
clulas in Trianculo ABC. aequalica.
cem circuli D B. cum Triangulo ABC.
deductione maxis speciosi quam loli-
da, ut ex dictis patee, quancumvis ac-
cidar conclutionem esse veram. Addet
anobis proposita merhodus figurae ip
lius unam periphieriam OX. eC unam
rectam EHI. Parallelam laceri BC. _
arslo. Ouoniam lincae sL. _ FH
Tun

## Folio  -  — 782001750:0030
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n
FXERCIATIO
une aequales periplieriis OI. de OX.
et pars radusF, communis mensu-
ra lacicudinum Annuli GROI. ee
Traperii EFL FT. aequalis cs lrape-
2ioannulus, sc lic de quocunque de
es
quorcunque annulis e craperus limi-
5
licertormacis. Sed omnia Traperia
line dittrcultare (une aequalia Triongu-
lo d omnes Annuli circulo; eroocir
culus DB. aqualis cst Trianoulo
ABC. Videreisitur est, quam levi
mucatione methodus indivilibilium,
quando solide procedit, in notram
mechodum de lele evidencem, con-
verratur. Indivilibilium itaque Geo-
pi.
meclanihiil opus ett, (nam de Arich-
metica indivilibilium nihril habeo
Pronunciare) Racura univerlali me-
thodo conscribendi Axuras, quae mu-
catis mutandis juxta materiae quali.
carem per omnia pervadit e ubique
milicat.
Unde non lacistacit mihi eleoan-
tissimi Geomerre Fvangelictae Torri-
celli restrictio quod in planis quidem

## Folio  -  — 782001750:0031
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 25 lines, status machine
GEOMETRLCA.
ticuris Colae circulorum peripheriae
in Colidis autem superticies cancum
modolphaericae, crlinar. cae, conicaeq;
idonea lint ad demonttrariones. PTinus
quoqiplacer atsenara racio quod Iola
iltae pertecte adaequent fixuras, ex con-
Ciderentur tanquam undiqu aequalis
uniformilqs ipillicudinis. Cur enum
o
elliprica hyperbolicaeq: _ quarum.
libet regularium Rourarum live CIr-
cumterentiae sive plana, de corporum
ex IIS nacorum corrices non eandem
vocentiam obrineane, vel quid sic
quodper spissirudines vocem velic Cx-
primere, prortusisTOTO.
Spiralem. Archimedaam esse aequalem
Temiperipheriae circuli pri-
maerevolationis.
Uoniam probarum estper quan-
ta posse expediri illa que per in-
divisibilia uciliter tentantur; exem-
plum aliquod resule proposex exhi-
DCTE

## Folio  -  — 782001750:0032
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 XF RCIL ATTO
a
bere conlenrancum eric. Fcne opera
vanereratur, convertenda elt ad lub-
jectum quodsciencir ampliandae Ter-
viac d non cantum oltendende.
F. 3. JEso iraque angulus rectus ABC,
Cut OpposcuS lIC arCUS AC. QuaETa
parscirculi, ee bilecetur per lincam
BD. anculus _ arcUS, cujus dux me-
dicrares sine AD. DC. Bilccentur rur-
C
Pus arcus e anguli per rectas EB. 8
F B. Bilecetur item AB in G. _E CeNErO
B. Spatio B G. HaC arcUS OHI. lCCaNS
rectam DB. bitarium in FI. _ crie
GF. dimidius arcuS AD. SC quarta
parSEoTIUS A D C. 8 duo arcuS OHI.
e DC. una quaria parce hoc elt IpSa
quancitare arcus GHI. minores inte-
eroarcu AC. Bilecentur rursus linou-
la PaxTeS AECUS ADC. perlincaS BR.
BL. B M. _ BN. BilCCCTUT QUOq: PG
InO. SE E D in P. BC duCatUE AECUS
00. donec lccet L B. dE arcuS P R. d0-
nCC(CCCEFB.
EC quoniam arcus GH. Pectus cA
a
bitariam in puncto P. Drecta B L. CTUNE
qua-
2
M

## Folio  -  — 782001750:0033
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 27 lines, status machine
GFOMETRICA.
QUatLOT arCUS OO, IHI, PR, _FC.
sic ordinaci, uc PE (c duplus O,
PR. criplus ejuldem, _ FC. Qua
druplus ejuldem O0. hoc est singuli
arcus excedunt le invicem uc numeri.
Locus iraque arcus D C. excedie du-
OS arCUSF C. _ P R. Und parre aequali
arcuioQ. a TotusarcusGHI. excedie
duos arcuso Q. d III. Una parce ae-
quali ipsi Oe. Duo itaquo aECUS
G H, _ DC. exCCdUNE quaTUOF aECUS
Oe, TH, PR, _ FC. Pecparrem a
qualem oobis, hoc est per parrem
aequalem dimidio GTT. Sed totus
arcuS AC excedit duos arcUS OHI, _C
DC per parrem aqualem cori OHI.
Excellus itaque cocus supra duas
parres cA duplus excestui duorum ar-
cuum Cupra quacuor.
Similicer, Si incelligarur certia di-
chotomiateri in parres leu arcus oeto
quorum primus lus E, quoniam SL
eA quarra pars OO. Medictaso
cum ipla ST Cune minores roca O
per parrem aequalem sP. de lc necesse
Ct

## Folio  -  — 782001750:0034
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
FXFROITATIO
ele linoulas seminas pro prioribus
guatuor Cuppolicas deticere a priori
bus quatuor lingulis parcibus sequa-
c
LibusST Propter oradationem conti-
nuatam secundum numeros Guatuoi
ItaQu DartES, OO, IHI, PR, _ FC,
 
excedune SI d caeteras leptem per
e
cerciam dictiotomiam tactas quaruor
parcibus aequalibus ST, hoc Cst, PEr
unam parrem aequalem OO, hoc est
perdimidium OI. Fxccslus itaq; qua-
tuor parcium seu arcuum lupra octo
es dimidius excessus duarum parcium
Cuper quatuor. Fcsic lemper. Si Itaq
dichocomia continuetur in infinitum,
C)
linea tacta ex primo exccu putaCHI
e omnibus medieraribus medieratum
in intinirum, es aequalis excessuitoci
EIS aTCuS ADC, lupra lincam quae con-
Jureir ex arcubus in infinirum multi-
plicaris per dichotomiam, & ordina-
tis secundum incrementum numero:
rum modo explicato. Quare cum GTI
cum omnibns mediccaribus faciac du-
plam OHI, hioc es aequale AD, CFIE
LIIIE.d

## Folio  -  — 782001750:0035
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 27 lines, status machine
GEOME TRICA.
linea hiujusmodi dimidia arcus
ADC. Eccum hic ipse discurtus pore
cori circulo aeque acque quadranti ap-
plicari, ee linea qux liC Ordinatur i hoc
cum circulo sic Helix Archimedea, uc
pacec exconstructione ipsius, AcHleli-
cem Archimedeam cAe dimidiam cir-
culi primae revolurionis, uc appellane.
PTaxIS superius data reoulae de
conscriptione Agurarum alceri cujus
quantitas sic invenienda, in hoc ex
emplo consiltie in co, quod arcus in
cinsulis mulciplicationibus faciune
noras longitudines leu quasi tiguias
Cx arcubus circulorum inscripris (pi
rali vel parri ipIuIS, magis e magis
ppropinquances Hlelica vel parulle
lices qualirae: Fr liccarpropolitâ quan-
cula linea, oltendere lonoitudinem ex
hujnismodi arcubus, differentem ab
Hlelica quaelica minori longimdinc
quam sec linca propouta.
Fividens ulrerius Ac demonstratio-
nem quae ab alignibus affertur ad pro-
bandum xqualirarem inter lineam
Dara

## Folio  -  — 782001750:0036
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 14 lines, status machine
+
PXERCILArIO
parabolicam e primam revolurio.
nem lpiralisnon esse Armam, cum in
e
Ca accipiatur Temi-circulus, culxequa-
lis estlpuralis, proaze parabolae; qua-
reparabola, necellario ex vicalis de
monstrarionis, Forermajorspirali, cui
q
acenditur demonstrall aequalis.
IN15.
1bs
irmu

## Folio  -  — 782001750:0037
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
2
Lecbri 

## Folio  -  — 782001750:0038
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
On. 1
219. 37. LeiBr. Mar9. 37, Suiet

## Folio  -  — 782001750:0039
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 4 lines, status machine
Leibn.
t
arc
d