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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 275, page id 845634801:0281
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X. Siert
20. Ouont
CX CrIIaq
rajormit
EOli
5, TI. IG
Duod
eranire Pet
d illud
in parodo
est de iM
rOrciona
CTa PILYL
TCT A
P V F 1
De construendo quadrilatero, quod sa on circulo.
cc epcatu elt ac perutise lroblema de Co.
t
loex quacuor datis recis CIS Guacaleo, iea
Culuscca Mn Peac. Lcopoluciunt al
ltelices ChirursiadidopusHoC LACorcid.
perint quatuor linea recta ex quarum prima utbase, e
DCundant perpendiculo, constiruatur trianculum unum rectan-
culum. Aque ex tertia ut base, es quarsa ut perpendiculo, con-
Huruatur crianculum alterum rectanculum, describatur aurem circulus cujus dia-
meter aequalis sit compositae dimidia ex hypotenusis eorum triangulorum, is est cir-
culus incra quem constructum ex quaruor illis rectis lineis quadrilaterum poterit
aptari.
Sincitaque datx quatuor rectxe linex primars, secunda 20, Ferria7, quar-
d24. Trianguli isitur rectanguli, cujus balisr5, alticudo 20, crichypore-
Aula 25. AE que triangulirectanguli, cujus balis7, alcitudo 24, erie tiypo-
enula 25. dux duxe hypotenulae conticiunts o. Dimidia isicur summa, id
C25, erir (le cundum Pheorema) diameter circuliinera quem quadeilace-
tum ex quatuor daris constructum porerit inscribi, ut revera est. Acinseri
larum Ordo nihil ad dic adimic. ve peripheriarum subcentioni. Nempe (i
Cetae 15, 20, 7, 24 Subcendunecocam circuli circumterentiam, subtendent
ordinc inverso qualir5, 7, 20, 24. Frianguliisitur rectanguli primi ba-
eltors. alticudo7. Frichyporenula v 274. minor ideo Y289 id est minor
olisitudine 17. Prianguli vero rectanguli secundi balis esto 20, alcicudo
+. exit hyporenular 976. minorideor +o24 id est minor longicudinc. 32.
Duarum itaque hyporenularum summa minor eric +9, atque adeo dia-
Herex circuli erit minor 24 :. Cum ante per eandemmechodum inventa
Friser 25.
Fallaxigitur ea doctrina est qua ideo non utar, sed reram quammemea
docuerune Analycica candide impertiam. Ab iplis vero ordiar Ceome.
prieis elementis.
PR OPOSFE10 I.
Cujustibet quadrilateri eria lacera sunt majora reliquo.
Exponatur quadrilarerum quodlibet ABCD,
constructum ex rectis AB, BC, CD, AD. SanC
Charum aliqua porest esse majorreliquis eribus,
Lerirmajor omnium. Sic major omnium AB.
Dico iplam AB minorem este COmpOlITA ex
BC, CD, DA.
Agatur enim dingonin CA, consticura igicur
e duo crianeuta ACB, AC D. Frianguli aurem cujuslibet duo lacera lumrmajora reli-
O. Itaque eric AB minor compolita ex BC, AC. Sed eipsa AC minor erie compo-
Ad ex C D, DA. Ouare canco manifestius AB minor eric compolIIa ex BC, CD, DA.
Duod erat demonstrandum.
PROPOSFTTO TI.
Si in quadrilatero duo anguli oppositi duobus rectis sint aequales, erit
Uadrilarerum in circulo.