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# Title: Pascaliana (shelfmark LH XXXV, XV, I)
# Folio [22]v, page id 00066632:0044
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00066632&page=44
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fig. 16. Pasiat. 2a) diameter. (4) Radiust B.
16
a
restabit:
(8 1412d
x
umma sinaum.
oe a
a Quaidratum diametri
(2 4) quad insciptum (R4 2 a) Rai tati isqe
ejus dimidium G7, R42, a = Rg, a. 7B = a - R4 : a. Ducatur ZB in arcum gB.
Erit portio superficiei cylndrice, cujus basis circulus AB.  altitudo ipta 7 B.
peripherta oetantem.
ponatur ZB. duci in totam peripheriam, manisestum est cylindrum, cujus est ea superficies fieri
ex ductu circuli in buseos in altitudinem cylindri. Radius est a. Esto Peripheria X. erit litus
civculs: aX et Z colinder erit aH, a - 19 L, a, = ax - a x _9L, - an-a x ax- as
aqu
Area cylindri divisa per bac semibasi, radium baCos AB= a. producto duplicato dabit superficom
cylindri, totam cuus octara pars est, dicta portio qu quaesita ergo dividatur perradium, producti,
R9128
ab hac si auferatur summa Sinuum versorum
X9. XD d seu segmentum, duplicaturo, B duplicatum, restabit summa sinuam rectorum DR. DZ. BB
 dupl. Jamquia segmentum circuli majoris non potes commode auferi a minri, auferatur a majore
a
calum est ax- a ause
ratur ab
ax ax
B
vel AZ
8A Sumatur pars, quarta aX = aX
Segmentum daplitatum est
aX - ax -
 18
eis
e
ax
et a Residuo auferatur differentia inter majorem e minorem. Nam si auferre debeam Bb ab a.
idem est ac sianferam b a C. quod esse suppono majs quam a. et a refituo auferam disfe
rentiam inter C et a. a - b = f - b, - ( +a Poro segmento duplicato PB. ablito a
Circulo AB. restabit semiciremlus aX + duo Triangula octantis circuli tutera. Ab hoc
residuo auferenda est differentia inter aX et a+ = at
seu
ectabit
28. T eu
q
aX + ax - a p
2
A4128
BaK + aX hoc auferatur a ax + 2 V la octortis AB - san ax- 2 ax.
R9128
Restabit: 2 a octantis AB = a 
ax. Ut autem investigemus Flum ostantis habemus
adda
R4 128
rectum 2Z= vel 2T. = Bq: a. Xeius quadrato: a. anfertu tum de ZB. a + 1 = 2a 14
habemus 2a - 2a  R9 , hujus Aq. est Recta (QB)F
2a - 2a
2a- a n4, eit
a2 auferatur a quad. radii a. restabit titum fuleri Ergo fulem erit quod
a a erit a--
a + 242
2a- 2 a vai = 4 2a + 2a ni
Et fulcium eii
(uppue fulem aequari recta q B) ducegtur sim siidiu rs i dimidum
EB. productum erit quadrati ZB. dimedium ducatur in QB. productum erit R9 4a-Aa
=
a7
+ 2.
a- 4a
a= a
= (4
n.  Eriangulum octa ntis
Jam omnes sinus D1. aequantur radio a. ducto in Da vel 2Z = Aq: C a fiet (R91 a.) summa simmum
2a
q
64
32
a o auferatur recta ZA v (vel 22) dacta in arcum,  ZB vel B fiet Rq ax, restabit.
p4L a - = 24 2  ax = - 2a. = a X - ax. Ergo (quin R :  ax aX ) erit a - 2a - a X
∞
54128
2932
necesseest errorem esse in calulo, quia a J2 2a
A432
29128
RG2 (932 8
Quaora
chordan
cujus
quadro
alterius
a - 95 a, 2-
a -  2- 
14120
a
idem producitur, si a et
-
a
a at
auferati
iq
= Z. a
42 = 8 R912.
qu qu A412
a
Eornm
padis
um
Sinun
a his
radio
est
e jusu
d qui
ecil
qui
est in
ecta
3R
seu
st
de
sit
sini
sum.
laec
quod
sipil
ium se muluo tolllere
in
4
20
calcul
14
a 2a
am
R42 A932 142
2a 124
B432
a
auter
fortasse dalur Meterodus in arithmetica infinitorum, summandi aliquam suddorum progressionem, quonia
etsi praecise inbyris expitui non possint, for aliquando tamen id quod dast deest, erit minus quolibet
dato. viy. quoties res reduri st ad pum statum, uts
ab illis pendens desit
persitque ed enim tuto negligi potest
R4 a. + R9 b. R4 a + b. + 2ab.
A9 ab. + RgbC = RgC ab + b7
21
abc
aut aliquid
2v
eq aet R Bu a + bC + R9 d + bc = Rgu a +bc + d + BC + Rg bc +bc a +dbC +di1
quoties muilliplicave duarum surdarum in se invice aliquis terminus produci potest,
ex quo possit extrahi radix, suve quadrata sive cubicax. torties extrabus
sundis fieri ptso una
differentius ins dras rugices quadratas semper exprim potes, ine raciis quadratam vag.tiq ab Rb
Nam
Rg ab RqbC
pa ab = leste
+
bc
R9
Nota sii velis mire summam quatruorum, sic procedendum ab- bc
est, ineatur summa quadratorum, eaque duplicetur producto addatur
summa quadratum differentiat
erit summa Radiamo
4b  Rqr.
e duaae
dices
resia
m quadra tadis
jam si his radices summare velis,
qa Rqb
a + ab = 2B aqu - 19b, 4 B4 2a c 1 2bE
+n4C
a+ 4b - 2CI Rg 4 - R9b
rae oC+ rCE
ser
1
pulo
ipsi
ulto
ds
seu
este
Cy
quadratae differentiamus
ca - 1 = A +
= A + V
B- A = .
= A.
B- A- X = 0
= 2
sum