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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 362, page id 845634801:0368
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.88
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V A R XORYM DE REBVS NIA YH EM A TFCIS
Elenchus Syllosilini.
AE vero libete aclatur AF per quodcunque segmencum circum terentia CB. Trague
sequeretur quam cunque circumferentiam FB, modo Faciat parrem ipsius hexagoni CB
elle amplicudinem sexeimxe parris duorum rectorum. Iloc aurem ommino est ab lurdum.
ERigicur in expolira demonstrarione aoumorsia.
Conclutio secunda prorlus vera est, e syllogiltica.
Ac in prima Fallacia est.
Erh enim quae constructa sunerraperia LFBC, BFIK CnE d Bene demonATenETR
quiangula, non ideo laceribus censenda sunchomolosa. leaque criangulum IBG trian.
sulo IBR male concludicur simile.
Lacus quidem IB urrique rriangulo commune est d angulos IGB, IRB subtendit X qua.
les, verum angulus FsB angulo BKI nullo casu porest esse equalis. Idem angulus FI
angulo BIK uno solo caluporest accidere xqualis, videlicet, cum angulus F. AB duarUIM
CA leprimarum recti. In aliis calibus quibuscunque inaqualiras cA, ex lacerum conte
quencer disieo, Casdle porestira demonstrari.
Cum CinEinerianGUIOAFB CTUTA AF, AB aequalia, uFErque anGUIOTUM AFB, FBA, leu
iis equalium AIK, AIEL desicir arecto per semissem anguli F AB, seu ei x qualis IBA. A. 9u
incrianguloIHIF, quod simile constructum est ipE ABF, cum GnECrUTA HIL, FIF aequalia
UEEFGUE anGUIOTUMI HEL, LIIF, Ceu iis aequalium EBC, HOB deficit a recto per semit
sem anguli LEIF, id est anguli F. AB. Ouare ansuluS FBI, cui ex rarione parallelarum equa
lis est BIK, deticir a recto per sesquialrerum anguli FAB. Angulus aurem FIB duplus l
anguli FAB. AC denique angulus IKB seu BCI, quem angulus IK A vel BOFI relinqui
e duobus rectis, exce dic rectum per lemissem anculi FAB.
Acque adeotriangulor BIG, IBIE anguliica le habebune.
Anguli trianculi BIC.
(recto plussemisse anguli F AB
anculus LB C aequalto sc, recto minus : anguliF AB
duplo anguliF AB.
Anculi trianguli IBR.
(recto plus semisse anguli F AB
liphi anguloF AB:
Non cHcisimmr angulus FIB aequalis Ahgulo BKI, neque enim duplum est aequale lin
plo. Ilcrique vero, sivc angulo FIB sive angulo BIK, ad datur se lquialcer anguli F. AB. L
plus igicurangulus F AB cum semisse ejuldem aquabiturrecto. Itaque in alia prop
tione quacunque anguli F IB, LB K crunt inxequales
Omninoxqualicares cubicasnon adgnolcie Gcomerria suis concenra Coliris postulatss
Dui aurem celteradecasonum describit vel hepragonum, in xquarionem incidie cu
cam, ur estin Analycicis exposirum. Acque exjam construco Mechanicaratione letu
mare lic porest demonstrari. Hlicisitur etto
PROT ASTS IV. THEOR F M A.
Si angulus acurus erianguli reCtanGUILI FIICTIE SEpFIMA ParS LCCI LOVUI
Cub hyporenusa dimidia et quadrato perpendiculi, minus iplus perpet
diculi cubo, aequabitur cubo hyporenula dimidix, minus solido duxlo 
Perpendiculo e lyporenula dimidix quadtato.
Siccriangulum ZFB, habensangulum ad F rectum; ad Z. vero aqualem seprimxe parc
recti, a secerur Z B bitariam in A.
Dico tolidum lab AB ec quadcato ex FB, minus cubOCKFB, aequare cubum ex AB, a
nus Tolido duplo lub FB et quadraro ex AB.
Cenuo enim hincervallo AB eu siL. deteriburus cireulus. Circumtereuria is c
liud
362
TKD
RV
Anoulus BLK aequalisAe recbminus se squialtero anguli F AB
tium
d
A
110d
1ad
d
Udi