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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 255r, page id 00067993:0511
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ad calulos redacere operae pretium esst: tatet quadoatum BC=. CD BD. sam summa vnim D= a
tam ut habeatur summa quadralorum omnum paralletarum basi BC, ipsi ACq applocatarum, inveniatur primum
AErgo
summa omnum quadratorum ipsius D racii,  CD, ad AB. dapplicatoeum, sive demta summa omnium BD.
Summa omnium radii quadratorum, ad e AB. applicatorum, e posito AB. = . et CD - a. erit a b.. Summa
omnum BB ad AB appicatorum est  a  a- B.  a. 26 eti  - est ab +   - ab
Ergo simma ognium
1 Ergo BC=
a - e
a- 23
a + at= 2a a t 4( 4Ba etc
uel a. + a + a,  5. 1. et f 2pa ,  a. + p a.
asb = ab -  6B A ab. Eg AC = sua sumus omnim BC = ab - +b.
entum
Hanc summam ne repetere necesse sit, appellemus, (C3.)
q dimidiatam, se
Jam ut quadrata omniam AB ad ABC applicatorum, habeamus, ita piscedendum est. dantur quadrata
emnium A parallelarum AD. ad DEr applicatarum, seu omnium applicatarum totius quadrantis, nompe a- = a.7a
dantur et quadrata dmnium applcatarun Aortionis EL C. ipsi CL. pabullelarum, nem pe  A a EL = 3 Et. quam
Ergoa = a a EL + t Et = summt omnum etorum applicataum quadriliuer et D A FC. ipsi AB pralleta
staud ne quaeritur, jam summa omnium quadvatorum, applicatarum segmenti CDA, ipsi AB. paralle larum.
et manifestum est ABi H BD + AB BD = AD. idemque est in omnibus parallelis. ideo deo
idco AB= AD - BD AB BD. vel quadratum parallelie ipsius AB. aequatur quadrato parallele ipsius AD.
s sicatu
uare et smoip quadratorum omnium parallelarum ipsius BDd. Caquatur summae Otorum, omnium parallelarum AD. demto
aadrato BD. ducto in BC. seu demto BD X demtaque praeterea summa omnium AB. AB parallelarum, id est satio
e A vel semisegmento ABC. in BD. seu cytindrico culjus basis ABC. altitudo BD.  pono ponamus BD(4)
Fiet ceumma quadratorum ciptus parallelarum AB = = a - a EL + ZEL - BDDC= ABC VD. est
antem EL a - BF fiet : BC - A - EL. fiet.
abD = Bd Et - - ABCBD.
vel qua cL = a - Bc. fit: 3a = a = abc + , a 8 + a - 2 a BC , 1 a BC = Be 3 - BDBC, - ABC BD.
Et = a + BC - 2aBC.
4. a + aBC = 2a BC - a. BC - BC + 2abC
1
a EF
EL
vel a = 3a BC , 3aBC - BC  totind autem istud
Za = aEL F1  EL, - 1B BC- ABC EBD
apecabimus (d3
ABC BD.
et quia sector circuli, ACC D. est curva ABC. n votum vadium A. ideo curvam appeltatins _., erit sctor 1 ax.
a quo auferatur Plum DBC, = OD BC, = (e.) erit segmentum ABC = ax - C. et ABC 1D- ax - ea.
p apt
segmenti ABC ex bati BC. erit:
d- ax + ea. Ero FG d- ac + ea
lam d ducatur parolbla ipsi BF. ex centro B. nempe DH. intelliguent jatu lacta, et ad cau perpandinearis BK. actoque spatio
ABC. circa axem DH. monontum ejus erit: aX C BK.  Investiganda ergo BK. ex datis, quod ita facile fiet: Triangulum
BKD est simile triangulo BGF (est enim simile Vlo DKM, et hoc Vlo DKK. DNK, et hoc Vlo DLO et hoc Do BGF)
ideo DK = FB BG.  posito BG = (7) et BD - (9) fiet BX - et FB - (Y)
iem alite, quia Ilum BDM simile Vlo BGF. etam Vlum MGB simile erit Vlo
ergo Bk = FB
BG cognita BD. cognita.
BD
DbDGF nto quia augue, MBF rectus recta FG puducta cincilet in M ergo DM = BG. et D = BF
fiet: BH = 2F.
sen It DM B et simile Vlo BGF. poo e sic ncipotes. BX. 31. ideo Bk = BD. g 2. 9 - 
n
cader in M
uter
BD BM
B. falsum rectam DM. = BG. ideo falsum et rectam BM esse cognitam. Sed
hcmittamus, patet hine:
45 yf+
(axyF) momento semisegmenti ABC. es axe HH ki
Iiem momentum u aliter innestigemus. Cum autem st sit +
29
l axteas
y+ FB sit Y BG + FG. et FG_  per
 eut G= vel pro 43 + e a fpundos (1) fier (F5) 1+ asx, et rG= 1+ atX xi aesx
2C
.
fC
fiet FG= i + ZX = RX. jam BG = fi. Ergo FB.
Erpo(FB-) sfi- 1 7X 4 KX = (Y ccu mogeatum smisegmenti aXyf 1 A ducentum pro aF. substituatur 
n
e
+C
 ∞
D Idem vero momentum aliter
in quae mimen ducta axf dant
BXIBEX RXS d.
Ac inoestigibinus inderounae, quaenus nomentum Empegi lo KBAB _ sive Rectansili KQ. et Bli HZB.
fitt ouea tiarrisno segmendi = L fx - il
ac pimum
Rectanguli