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# Title: [Quo Continentur Claudii Ptolemaei, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunae, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Graece & Latine Edita, cum Notis ; Accedunt Epistolae nonnullae, rem Mathematicam spectantes; Et Opuscula quaedam Miscellanea] Quo Continentur Claudii Ptolemæi, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunæ, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Græce & Latine Edita, cum Notis ; Accedunt Epistolæ nonnullæ, rem Mathematicam spectantes; Et Opuscula quædam Miscellanea (shelfmark Leibn. Marg. 100:3)
# Folio 28, page id 867984570:0056
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CL A ED II PYOL F M A. 1
Cap. TF.
distancia elt minor; substituatur aurem in illis, on HaegnapBare  En avrcv, avri rys
pro densitace, rentio, (uc quae roborat e indurat:
unde similiores redduntur Chordae eis quae FunE
in minoribus dictanciis;) manifestum elt, quod
(cxceris supposuis paricer se habentibus,) ut
est cenlio major ad minorem, sc qui est in ma-
jori Ponicus ad eum qui elt in minori: UE au
rem major circuitus, ad minorem; sic, qui in
minori tic Conicus, ad eum qui in majori. Dico
jam (his ica se habentibus) quod, dissimilium
chordarum, quando tacta lune in dictantiis a
qualibus aequitona, id quod proxter majorem
circuirum Lonicui deest, ab eo compentatur quod
HOKVEIOECOSS n raorS 2010 gd, nat d oxnyeuvet
n 9. 7370  paMev cior F ev Ex a eo2 3)45_
ocoV OuOtaI AnNOV ESIV, ort, 5 aM cr LWONCI
pducor Tcr aorcor, cos edi inn coneicor ziveras raors
95 8 Enaora, STCS o nara 2 onciova il
DO We5 Y nara F Exarova ios n peie con
oECOXI NEOS t Exarora, B ircS o vare T ENar-
rova oDO nEos + nar Y pciCora Neyco dn.
FETCY BFCS ÉXOVTCOY, on, 5 arouoicor Zopdcir,
vraer ex ioc5 ZasaocO iocrovot non dor  ay
propier majorem centionem redundat: aique saeva codnesr, X cd dg + peil ova  EOXHV v-
omnino tic, eadem majoris circuicus ad mino. Déor s Vops, 5 2 9 tW NCIOVa TOI LE
rem racio, quae elt majoris tentionis ad mino.
rem. Sunco enim, in lonsitudinibus aequali-
bus, aequitoni Coni A et B; licque iptius A
quam B circuicus major: maniteltum elt, mi
norem ese centionem iptius B quam A. Suma
curque alius, in eadem longirudine, C; qui cix
cuicum habeat eundem cum B, tentionem vero
eandem cum A. Quandoquidem isitur C d B
cola centione diHferr; erie, ue in C tentio ad
centionem in B, lic Ponitus C ad B tonitum:
Icerumque, cum C ab A (olo circuitu difterat
exit, uc cireuicus A ad circuitum C, sC C (O
nicus ad fonicum A. Sed eandem habet ac
utrumque rationem C. Ponitus, nempe ad A e
B (aequales utique Tunt A et B ConitS.) VE
isitur centio C ad centionem B, Sic A cireuitus
ad circuitum C. EAque, ut C tensio ad ten-
Tionem B, Rc A centio ad centionem B, (x9ua-
les enim FunE A _ C centioneS:) uique Cir-
euicus A ad cirenicum C, sic circuitus A ad cir-
cuirum B, (aquales enim Tunc B et C. cireuitus.)
CaMorr i Zve) narrcos, o ∞ peCoO coEi
XyS rEoS Y Ena Dova Negos, d avros Tu F CoNeto-
VO raorcos reos t exe Tova. ESCaV L yd,
et
lovis poyxeoir,  iovrorot duo Ddoysos,  oi à e β
i peetE cor n 2Eroxn S a + S B. Kai P dnnor-
on 22 i rao15 eactcor, n S B no5 rli 
a. Einipco re a O, er isco pinxe, oy. +
ed oeroxle ionu excor reo B Y ŕorr ion rio
à. EEt roiv o y S B poon rn raod 3a Deper
Escp cd5 i S Y rasIS neos Y +8 B ruW, 8TC5 a
r8Y 10 9 reos Y rS B Loper HaNWV Exet
oy rs a rn euoxi uoon D) a. DEpce esa i05 n
28 a Wecozn neo5 Y r8 Y Wecoxlo, X y rcoS
5 r8 Y 10D6 reos Y r8 a Vopor. AM a Y
auror exd negor, a r8 Y aoDO, neos  r ena
rep3V, 2 riv rE 28 a X Y rS B, opov 1001 qd
et 2 a n, B. S5 ae n rS Y raSIS XpoS rud rS
B, ircos n 28 a WE OX po5 rlu 28Y. Kai
EGW co5 edi n 2od Y FaCIS reos rlo rod B,
ixcos n rod a  rasiS Xpos rls 28 B iocy yd ai Y à n Y raods 15 de n ru à oec
_ reos rlo nd Y, ircos n rod a coerx eos rluo rod B iocet id ai rior B ig Y roEcoxai.
vele cor aoecozii.
major cireuitus.
Rat
Encesicor adeto .
Nei cor reors.
Masor 1
minor circuitus.
minor cenO.
sato dyropsis.
Data.
Concindo a= 1B - 17
adus.. a
CrCMuS y = CB = ba
Censio... v = 1
ExeeNCN TaOIS
Demonstrata.
+v. +B:
y (= 14). FB:: 64. c7 (= cB.
Ea. tB:: 6a. CB
AB. 3 imi. C. 3 int X. d ABC T. ondrpaires. O. onncipes. e CV. Eoi uo. AB. decA er. S. po m er chat
or Dlasuoro om. FC. i 3. 5. ougicos 3. 8 S. deest eras o n u chcartora. B LV. avo
i 3. - - pur2a
dect 7d. 15. dces ev. im CO. ivoronos 17 17301. KV. avo --. 5. d0o 8) ey70c 10or. n AB. n. 0CGISOV. iro
C. dunoron n. q V. deest C. r CdV. deest enartar, n _ B avess rd _ a sABC,O. 5. +S. a c5. W PrO rud
malim rn 5, bis. x CIO. ira y O. decst r. 2 CV. io n. a CdV. decs opor. b K. perperam ion gd i Y
AC B miors. C ABRS. perperam coeloxi. V. perperam inserie adeloxi cess std X qu C tsn as p n V Y. SC mOX
omierie ivns zd ni  a C y mous - ereos rd _B. d6(O. 8.