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# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
# Folio 222, page id 779785487:0280
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PH ZSTCF TRACT. TTI.
Priparabola GFD; eric Spatium aC-
quisicum in 2EcenTu COnUS MMIXEUS
Sub Cemiparabola FDC et alcicudi-
BC FA, qui est ad dictam pyrami-
demm inixtam vE 32. 2d 60. vnde
paulo maius subduplo; hic aurem in
plano, F1g. 53. criangulu DGRFI, Cst
Cubduxlum Cemiparabola AMOD.
vel DCLFI, quia haec est ad se-
ctangulum IIO, Ve 2. ad 3. igieUE
ad trianoulum parabolicu OLHII,
aquale GKHID, re 2. 2d 1. igitur
secundus descensus, qui est Cem-
ver aqualis praecedenci alcentui,
est Cubdoplus primi, in semipara-
Bola FIFD; sed primus descensus
est prima vibrario; sccundus, Ce-
cunda; ac. igirur lecunda vibra-
rio es subdupla primae: pari modo
sccundus alcensus Hc in triangulo
Parabolico DFO A, CubduploCemi-
DacabOLA DFTE; igieur descentus,
qui sequitue, aequalis pexFato
eriangulo, sc in Cemiparabola
ANIED, Cubdupla Cemiparabolae
DEFI; igicur cerrius delcentus est
Tubduplus secundi; igitur cerria
vibrario est lubdupla secundae, at-
que ica deinceps: Elinc tota e
integea ribratio prima, compolita
Scilicet ex alcensit d delcensit, est
dupla corius secundae v. g. FOT2 A-
GUTA AMOITID, eM dupla to-
EIUS HIFOAD; re paret; nempe
re descensus primae, est duplus
descensus secunda, ita alcentus
prima, est duplus alcentus lecum-
da, ve perspicuum est; hinc quae-
libet vibrario omnes. alias luc.
cedentes adaequar, E intiniea funt;
quia vero Anica TUINE, DE PaTCE ex
Mlecaph. quaeliber ribeario caneu-
lum omnes alias luccedentes lupe-
rat; hoc constar ex Arichmeticis
progrestionibus; sic enim ralis
3
Xc. ita ve quaeliber Tublequens, siE
subdupla incecedentis, secunda
deticie =. vel . ad hoc ve adx-
quet primam; si addas terriam
dcest adhuc Z. vel . C quartamm
F. decA adhuc =. vel =. ec. vnde
rides addicu semper ese Tubduplit
relidui, ad inreoram adaequario-
nem requilici; sed de hoc alias in
Arichmericis: hinc numerus vibea-
cionum non porest detini, repaTeF;
igitur neque tempus, quo tOca
series durat; hinc nonullos rciicies,
qui haec eories intrudune, quae ca-
imen Cciri nequennt; e Hxc ex hy-
pocheli semiparabola dicta Luneo.
PROP. CCZ  ZXTV.
Data ratione longitudinum, faci-
le cognosci potest ratio crassiudinum
Scilicer veraque chorda appenla,ad
iustam bilancem; uint enim chor-
dae eiusdem longitudinis, A craCTIOI,
Bminus cralta; appendantur; dico
rationem ponderum, camdem elle
cum rarione crassicudinum; nem-
pe cralsicudinem hic accipio pro
bal; quod s1 A Sc longior, ita
diuidatur oraniras A, ve habcacue
grauitas comperes leomento xqua-
li chorde B; St procedacur velupra;
denique si B Ac longior, altuina-
tur grauicas segmenti B aequalis
chordae A, _ habebicur intencum:
Tuppono chordas esse ciuldé mare-
rix, alioqui res non ita luccederet.
PROP. CCZZZV.
das diversa materia spectant:
Hlaec ve melius distinguantue in
cerros numeros distinguo. Primos
Chordae replurimum duplicis ge-
neris Cume; ex inrestinis Ccilicet, 
22
Explicari possunt quae ad chora