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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 161, page id 845634801:0167
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 75 lines, status machine
# Lines: 75 recognised, mean confidence 0.83
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# After the first blank line: the recognised lines in reading order, one per line.

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Pheria; CH quoque ee C B eriensperiphCHa D L. Guare cora peripheria B D cer merietuE
Locam peripheriam circularem, _ puletes comencum B C segmentum B F cer merie-
LUE, ducantur aurem subrena B D, D MI, MF. Ouoniam igitur B D; D M aequales
lune, X est AD circumferenria quae relinquitur sublata BD circumfereneia ex semicireu
l0, d M B ea qua relinquicur sublaca dupla iplus B D ex incesro circulo, estigituF M B cir-
cumferencia dupla iplus A D; aegui, ip EM B circumferentix, aequalis est circumterencia
FD, (2quales siquidem (UnE SuBEEn (X BD, D MI, ipAISDMI, M F.) quare circumferen
cia FD, dupla ericip siusD A. Sececuricaque circumferentia F D, bitariam in E: erun
IGITIT CITCUIMFCTEMLIX A D, DE, F. F aequales, de circumferentia A F ipsuS A D eripla
lubrendancur jam rectae A F, B F. Duoniam igicur eriangula rectangula C lB, AD I
Cimilia lunes ericue B Lad BC
ica AIad A D. eAt aurem B L dupla iphus B C, igituE _E A
ipsius A D dupla erir. Est aurem ex demonstraris a nobis Fheoremate sco 2d Angulares
Sectiones, ur lemidiameter ad iplam A D, id estur diameret A B ad ip (am A L, ita A D
ad A B minus BF, quare AB quadracum minus AB in BF, aequabituT A L in AD, hoc
es A Tguadeari (emisi: e adhibica conoruametathesi, AB quadearum minus A L qu2
drari semlle, equabicur A B in B F. Icerum ex iildem eAt, ut A B ad A I, ic2 BF 2d A F Ni-
vuS A D, rectangulum igIEE A B in A F minus A B in A D, aequabituE A I in B E, ergO
eadem ad sumpea alcicudine BF, cric uE A B ad AI, ica A B quadcatum minus A L9u2
draci lemisse ad a L in BE, id est ex secundae aequalitaris analosilmo, ad AB in A P minus
ABin A D: de omnibus duplacis; A B quadearum bisminus A L quadraro cric ad AB in
A F bisInHHAS ABTH A DBIS. _L AB ad A I.
Est quoqueue A B ad A L. ica AB quadrarum ad A B in AI, vel AB in A D BiS: quare
Esimilibus similia aaaAML, eIC A B quaaraCUM CeinuS A L quadraco ad A B in A F
bis, uE A B ad AI. ACprOIdC AB quaalalet in AIminus A L cubo, aequabitur A B
quadcaro I HL OIS. Ouod craclecundo oco ostendendum.
Tecrio: prorratacur ipla AC quancum lacis in C, de Aac B C dupla ipsusBC, quare
iphusB C laceris alterius circa rectum, porerit C C quadraco criplum laceris B G, perpen-
Dicorursus, Colidum eriplum sub A B quadraro in A C, minus cubo ipsUS AC, aqua-
(quandoquidem in criangulo reclaH C B, latus C B oppolicum recto, saruitur du
Plumlareris B C circa rectum.) sus B H C cerria pars est iplius anguli B AP, PCu PC.
cipheria BF, eric angulus A BII, sire peripheria AH cerria pars periphetiae AII F. de quo-
niam eriangula CHI A, C G B Cimilia (UINE, CrIF C A ad A FL, uFC B ad BG, es aurem C B
dupla iphus BC. quare C A ipsius A HI dupla quoque eric. Secetur jam peripheria HF bi-
Cariam in L, dc duicatur recta B L. CrUNE SEGMENEA A FL, H L. L F Xqualia, igicur ex demon
lraco a nobis laepius ciraro Theoremare, crir ur semidiamerer ad A FI, id es A B ad A C
ITA AFLiphuS A C semisisad B A minuSBL. OuarC A B quadracum minus A Bin BL
aquabicur rectanoulo A C in A II, id est A C quadrari semistr. R ursuS ex eodem FheOrC.
iIBace, uE A B ad A C, ita BL. 2d A Fminus A FI, de rectangulum A B in A P minus AB id
AHI, aquale erir rectangulo A C in BL. eadhibica congrua metachesi in priore aquali.
cace, A B quadrarum minus A C quadeari semisse aquabicur AB in BL. ErgO ad lum pT2
communi alcicudine BL, eric A B quadearum minus A C quadrari semisse ad AC in B L
ddattede Cimilia, eric AB quadracum ter minus
AC. minus A C cubo, aequale erir solido sub AB quadearo in A L bis. Ouod eraccertio
Acg: hinc constac lex ab Aucore estimodi xqualicatum consticurioni apposica: est enim
T6Y
L AB F.
Flcorimum circumterentia C D, anoulo D SuOEMI, IMenStOrMS CIrCULArIS peri
quum rectangulum sic criangulam BG C, e lacus B C recto subrensum angulo, duplum
ciculeeCer crianouli AC B
Et Colidotub A B quadraco ee dupla ip sus AL
OppOTEIS C AB, ACB, est aurem A C B cecta pars uninsrecti, sive semiperipheriae
Peorrahacur enim C B donecicerum circumferentiam secer in FI, _t ducatur A YI.
Duoniam ieague angulus AB HL exceriorerianguli AB C, aequarur duobus incerioribus
es ex posterioris aequalicaris analosimo, ad A B in A F minus A B in AFI, uF AB ad
C. de omnibus duplaris, erir AB quadearum bis minus A C quadeoco ad A Bin A P bi
minus A B in A EI bis, uE AB ad A C. est quoque AB quadracum ad A B in A C, vel A B in
AEI bIs  AB2d A C, quare similibus
C quadrato ad AB in AF bis, uc AB ad A C. Solidum ergo sub AB quadratorer ir
e ulcimo loco ostendendum
AB diameter, inlcripcatu axima.