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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 128, page id 1047377675:0144
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
# Lines: 31 recognised, mean confidence 0.92
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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BE
OPOTEMIE.
consequened ipsum rectilineum, quod demonstrare
CONSE CT A R IV M.
Tnc sequitur (A in rectilineo aequilatero quocunque
a a assignentur duo puncta ee ab eildem ad omnia recti-
linei lacera ducaneur perpendiculares) perpendiculares ab
uno puncto demisas aequales este perpendicularibus ex al
cero puncto demis.
P R O P. 69. T HI PO R F M A.
Si circuli circumferentia dividarur in partes quotcunque aequales es
numero impares, e a quolibet peripheriae pucto ad omnes eiusdem
divisiones rectae ducantur: (i circulus dividatur intres partesi
equales, erit summa primarum aequalis oltimae: si in quinque,
erit summa primarum es ultima aqualis summae secundarum;
si inseptem, erit summa primarum es terriarum aequalis Cumu
mae secundarum es Ultimae: si in nouem, erit summa primarum
tertiarum es oltima aequalis summa secundarum es quarta
rum; atque ita deinceps in infinitum.
Dicimus antem rectas primas esse illas, qua ducuntur ad divisiones
ex viraque parte puncto assenato proximas; secundas, iltas rectas
quae ducuntur ad divitiones primis ex vtraque parte succedentes;
tertias, quae secundis (uccedunt, _C: rectam verooltimam, il
Jam qua ducitur ad divisionem a puncto assenato remorissimam.
Iccirculi circumterentia ABC DF diuisa in parreS quOE
cunque aequales in punctis A, B, C, D, C, licg; O quod
libet punctum in circumferentia; à quo ad omnes divisio.
nes ducaneur rectae OA, OF, OB, OB, OC: dico summam
primarum ee vicimxe nempe OA usa OF  OC esse aequalem
Cummae lecundarum nempe OB. f. DD. Lix puncto O aUCaTUE
cir