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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 1
# Folio 4r, page id 00068018:0007
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5v); this page is its right half.
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X u
Mechori Taprentium inversae si netra 
ustiplicetur
alurus enex
X + il xy a2M X +
-lmy + n po in qua
xet X +ny -  H.
=gX = 219y + ingX.  t q
 id. . 1- - 2pa - 2 la . 1 m.
+ ulmgus-qmi
Esto jun aequatio ea V +. b Co + a 0, q. et proo Bponendto X + G pro  Cd ponento 1 +d. fier:
X AECX, + C + b s + ab d y rio
X F2CX + aOX + bY X + 2bdyX
Multiplicetur haec aequatio per X + XV = s: frei:
cujus ut voriginem intelligas, inspice figuram, in qua AB sit V)
BL sit cd. ACB, cura ad quam sunt ordinatae BL,
Et appellemus, p et quae ad curvam perpendicuearis est,
quona ponamus ipsins BB valorem sire relationem ad ipsam AB abscissa
veltione quadam aequatione expressam habert, ponamus exempli cauga
Br esse ut sinus descriptoque arculo ex centro A,
trea +roy +rbyadu
tan comferan do cemsnt.  quodurs tuus, atque dn sgentiunde
te sx regitivo
serivallis ab ordinatis .B ap
tmiam; adeoque Methodo Tangentium
inversa sequi figuratum omniam Quaedia
unnis et quadratiris, qu
(repitimms valorum Paa po talia apsicato renelim at 
n 3 + 2 n Ca
BE. percendicularium curvae
si his datis AB et BE, ipsa BL aequatio
=-b n e
Ego sive abn - ln - 21 ab vive n 5)a + (2- ati C
b sive ( lab + 1l ad l ad aebv
aH i sive 21Elabsi
l_ +2V ab + a b 0, sive l + ab p0. sive 17 Y- ab 
lies Ulnde n F
=ab  at 1 - + - ab 1, et rp- n s  ab.
-q- 2m s h c = s. Ergo Sp 2C + q. +m
exdata V, inventa erit co, unde
lq - ulma p 2bdo C bsd - ibca - baque ebam sivea d +) 2boa  baqtabam - bqm
otacien splibolae causa
+9  C lnd p et bd + +C
et 41
2b1) 2abm
CC( Ebca ( 2bam C fen n-
2bca Fba +2 bam (A 9) + 2m idcoque ds pca bad  bam selud 
(42mq+ m p aO - 2c = em. Ergo O⊓ met rCmt rCabl
El inque meq H  8a - 2b s
qui  sa6
En ED- dc + 2m
unde fiei : - 2l me - m l p m l + rem l+ C l - 2bea - 4bcam
sive m acmCV-bea  bcam B.
sive (Cm)p m +2Cm +2C, (D et im Ab Cm   (m + 25 + 2md 0
paulo ante praecedens: + 2m BC +8Cm 0
sve am C + 22 dBCm 7 A sive 25 4 n c me
Vergo 6cm +6ctn - am c - 16m e + 2m
sive dmY + (D C  (=4 m d ( 16  c) + 6 m jam 2C - 4m - 16 cm
14 c = 4 mt - 16c f + 6 mt 10. sive 42C = am 170
026C + 2 m 10
Quem. valorem inventum suplrius inserendo: fer y 3tt 10  0. quod est absuodum.
itaque in cum ad aequationem impossibilem perotuerimus sequitur problema sid quidem solvi
non posse. Ullud examinundum ert
sunt dequantitate, sed dequali Do excminanda restant, unum an alia multiplicandi formasteddi possit posibile; a alterum
vemonstae et haberictuo an ex ipsis impossibilitatibus sive contradictionibus aliquod duci possit ad appropinquationem
utisos (1) Nota si plena aequatio (duarum in cognitarum ducatur in penam, pinducta fet plena
(2) Si non pona ducator in plenam, vid omnis aequatio non plena latenus plena reddi potest, ut non
mery, nisi aliqui termini desunt, ex qui ex duarum incognitarum ductu in se invicem oriantur
licandi incognitas. nd Etx les aequationes vocibo Temiplenas. Omnis ergo
aequatio  non pena explicando reddi potest semipena, si utraque in cognitarum aeque
a ea pea ta b ab 1b +b
comnis sepriplena ducta inplenam satis etevatue fit p(h gradu inferiorem) fit
u n
alte ascendit. in
germicephala in qua una potetas summa nujus emcognitae inferis suuma alterius intognitae
 rane vos.
plena 
potestate est  nulla multixlicatione plena reddi potest
Ex Tserremate pringo et tertro junctis sequitur omnem semipbnarm ductam in aequale
aut superiorem plenam fieri plenam narm comnisplena ipsi aequalis aut altor siumilis est plenae
eoi quaedet
to ducta in plenvn. hugo eut in ei simil
Aeatio x + L y  m 0. Quad rata, idant:
quantum ad
B. hae propositiones non