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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 10, page id 1047377675:0026
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.87
# 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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reccangulum DZ est aequale mixtilineo P N 3 2; _ ideo per
mucando, uE P3 ad mixeilinicum iea R3 ad XF F, cumque P3
Sc maior mixtilineo, erie R 3 maior quam sit Z: eadem me-
thodo demonsratur 5 4 rectangulum esse maius quamo,
e Tdmaius quam ZA; es ergorectilineum RESN TudZ ma-
iusrectilineo it o2 Z SA R. Eodem modo ut NZ 2dX ICu
XZ ita 53ad93 Ccu ∞ Z. de permurando, veHz ad5zita
XZ ad o Z hoc cst ur 23 2d23 ita B Z leu mincilineum PH
32 ad FF _ permucando ut 23 ad mixcilineum D H Z 2 it_
23ad F~) Ced Qs est minus mixcilineo, ee ide07 est minus
quam +Z; eodem modo demonttratur 4 eReminus quam
ovo, ee nd minus quam ea: de ideo reccilineum vSoTnVdZ
minus estreccilineo FomZBAAF; _ proinde amborectili
nea t  _ v2 Z 6B a F. F oi n H pEd a  consictune incer
duoreccilii. ea HESN TudZ, SDTnVSEs hoc est maius priorum
receilineorum minus estmaiore lecundorum, de minus prio-
rum maiusminore secundorum; sed mixcilineum f o  SB
E consicticincer duo priora, ec ideo consistir criam inter
duo posteriora nempe RESX Tud2s ySOTnVd2 sedmixa
xilincum RSTV d2 consiltit eriam incer haec reccilinea, de
proinde maior est differencia reccilincorum RZS X I ud 2.
2SOTn Vo2 quam mixcilineorum R ST V S2, tit o  st a Xd
sed expolicione differeneis rectilineorum est minor quam as
de proinde differentia mixcilineorum est muleo minor quam
an quod est absurdum, ponitur enim aequalis; non igicue
differune mixtilinea RS T V d2,  o ZS a X, sed aequalia
Tunc, quod demonstrare oportuit.
Secundo nos eandem aequalicarem demonstrabimus in
primis Eguris, rbi supponimus curram R V in prooressu abd
R adV rectam 2s semper magis appropinquare, ec ccon
era curram 7 D inprooressu a7 ad D ab eadem recramagis
elongari; e ideo curra st sin proereslu a Xt ad st eo magis
clongatura recta F a, quonium eodem modo clongacur
curra s a rECTA  A, quo curva 7 D aFCCFa28. Sipra di
Et2