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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 70r, page id 00068200:0141
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et
puso ad probima
Excerpsi et hoec ex viota, ubi eadem ponuntur sed sine demonstrare
praemonet: Ex duobus angulis acutis trianguli is qui continetur ab
Hy potenusa et basi, acuti nomen retinete, alter qui continetur
ab Hypotenusa et perpendiculo esto reliquus e recto. (Hoc est
perpendiculum est quod subtenditur angulo acuto, basis quod reliquo
si sint tria triangula rectangula quorum primi acutus differt ab
aculo secundi per aculum tertii et sit excessus penes primum
sit trianguli primi perpendiculum D. basis B secundi perpendiculum . basis B
erit tertii perpendiculum ut Ap b tertii basis, ut :B +  p2
si sint tria triangula restangula quorum primi acutus adjunctus
eculo secundi aequet aculum tertii, erit perpend. tertii ut bp + pβ. et basis terti et bB- pto.
Haec duo Hjporemata ait vieta esse fundamentalia sectionum angularium
Hinc infert thecrema quod sequitur:
Trianguli rectanguli cujus a angulus acutus
est submulliphus sequentium Hypotenusa sit sit h. basis b. perpendiculum p.
in ti angulo angulissipli erunt Hypotennsa
diyhi Et
tripli
Quudenuli
Quintupli
ut
Dasis
perpendic
+ 2bp
Alim Theorema vietae in responso, ad Romanum
ubi patet eosdem prodire
numeros qui in genesi
potestatum, nisi signa
tantum perturbantur ut
in imaginariis
Nempe si loco 
p ubique poneretur +p
 summa ex
basi et perpendiculo
imet potentiam.
si fueriat triangula rectangula quotcunque aequalis hypotenusae
(nam in praecedenti nihil refert an varient hypotenusae)quorum
nimi angulus icutas sit in submulti pla raione ad ansulos spacutos.
succedentium triangulorum ad acutum indelicet secundi subduplus seu
dimidique ad aculum tertii subtriplus seu trifus etC. o et sit
seminius potenusad
simpili
basis trianguli primi b prodibit serirs tales
Pasis Afsunuli drpli B
sen sinus com–
jaculi
u
tripli
Quadhipiqu
quintiali
sextiloli
sempli 
octuper 
constlic
simpli perp
Quiatupli perp
sxtupti ba
spl
=27
2b
-5 ba
78
- 8f
nam 2 est ipsu diapmeler
+ 21
oncupli B - 9s + 29s
osittiis
es
pers
aspli bus
-3053
+9u
Hypolrinusti in casu anguli nullius seu
inficite parri
sit perpendiculum trianguli primi prodibit series tatis
+XR. - 2
suo s
p
9p
107
27 p
30p3
perpendiculum communi stylo est sinus, basis est sinus complementi, tyspotenus
pers
saltem ergo habemus generalem Methodum ex dato simu complementi a
alicuius arcus, inveniendi sinum complementi alterius arcus, cujus ratio ad
catum proposatus sit data, per Tabulam N
sit aequatio X aequ l+ m. X aequ l + SlmX = 5 (h X
l+ m aequ X
1. aeqo
1 au X = 3yX
lsgo X - 4yX + 2yy
15 aequ X - syx +5 yyX
b ep X - 6yX +9yX - 2y
 Aequatio ad curvam, ubi
lineo sinum in
arcus circuli in resta extenditur et
opplicaatur ei sinus
plementi
A abscissa est v, applicata X
conseramus Tabulam 7 cum Tabs
Gponendo y aequim aequ. 1. et X aequD
y aequ. 1. aequ n. seu M aeqo
seu 1 c l +1 aeg. 0.
seu 2Dc P+= cC aequ = cc -
seu quaego s cc - 1+=C
et m aequ. S: cc- 1 + LC
et Xaeqoe C+c1 curia
et geneuliter X aeq. t ex Scna Bhcarhcent
complementi aucus quasiti ad dutum
+ 146
eb
=16u
+205
mani
Angulidupli basis
+ 3bP
tripli pers
quadrupi bas
1B n aequ. c. Erg. + es