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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 3
# Folio 12r, page id 00067962:0023
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proposito 2da primi libui Euclidis
qua docetur ad punctum datum apponere lineam
datae aequalem, quae plerisque videtur inutilis magni
momenti est ad efficienda per linearum ductus,
quae ratione consequituur, cou inveniendas demon
strandas scilicet veritates, atque inveniendas constuctione
sit illipsers AYI verter A, focus D centrum C. jungatur
OY, ejus ducatur parallela AB intervullo. Nunc contro
Y interdallo A AO ab Nunc ab YO ex Y abscindatur
aequalis ipsi AO et recta juncta CA producatur dum t
ipsi AB occurrat in B denique ex Y in Axem. dei AO demitta
tur ordinata YX, erit AB aq AB aequalis abscissae AX.
Hoc calculo sic de monstratur sit alter focas F et jungatur FY
quia FY + C)V = AI et orit CX YX seu FY = A1 - OY fier
FX + XVI MA12 +13.
= FO AC + CF = AX
= a(YF 2. AI. OY, sed FX = AF-
et OX = XA AO = AX + AB - AC
rexa
AF + AX - 2AF. AX
Ergo ex FX +XY = A, + Oxhyfiec
CY AC + CF + AX + EACCF - 2AC:AR ZCF AX ( AI-
F+
CF
2AI. OY = AIYXY + AC+AO + AX + 2AX (F - 2AC AX 2AD AC
2
X
= XY = AC -CF - AX + 2AX. CF + 2ACAX - 2CF. AC
AC _
seu 2A1. OY = A1 + 4 CF. AX - A. AC. CF. seu AC. 3Y = AC + CF. AX AC, C
AoYB
seu AC: CF vel C =  AX: OY - AC + CF seu OY AC.
sautem CF = OC et AC = CF = OA et fict AC: OC = AX: (ra C: OX
et fiet AC: OC = AX:, OY - OA, unde si YB = AO fint DO = OY - AC
Sed hoc est carculo potius
ergo OC: AC = OD: AB seu AN
quam linearum ductu consequi veritatem etsi notae non Algebratae
sed Geometricae adhibeantur sed si quis lineis rem consequi veller
ver
deberet non tantum desciibendus erit circulus centio A radio AX ut
secans AB in B; sed et apponenda recta aequalis ipsi AC appo–
nenda ad Y ut centro Y radia intervalla. AC describendo drculum
is secet Y0 in A. ac tum ostendendum esset triangula BAG,
Oc esse similia si centro A radio AC descrlptus circulus
seret eA (Moductam) in (3. Notaadam quod circulus secet
u rrectam, lus, sed vatet unum tantum intersectionis punctum
noustrata
ioordintutarum quadratis
facile dnde demor
a qui
suptur tundamentalis illa, quod quadratum odinatae
et rectanus uto sub tl ndum constnte, et ea abscissa et sub
et sub residuo postat