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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 11
# Folio 18r, page id 00067970:0035
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Data Basi altitudine
et Angulo ad verticem
invenire Triangulum.
s Hoc problema esse potest specimen discriminis: inter
constructiones per sigure considerationem et per algebram
sit data pasis AB. altitudo BD inventas.
sit magnitudine et positione idata basis AB
altitudo at CF danta magnitudine seu
aequalis datae Bd. angulusque ut ad
verticem etiam magnitudine datus,
nempe aequalis dato E.
problema per Algebram, ita quaeremus:
Ex puncto C. quaesito demissa intelligatur
perpendicularis, CF ipsi AB basi productae
si opus occurrens in C. similiter ex
aliquo extremo baseos A. ducatur perpendicularis
ad latus oppositum BC si opus productum
ipsas AB Bd seu CF BC AC BG. CG AG -. BF
bocabimus. b
d
m. n
X
Denique quia ob angulum C. datum ratio AC
ratio AC ad CG. data est hanc vocabimus q ad 
eritus hanc ponamus esse eandem quae g adr. erit Z aequ F n
eritque AC ad AG ut q ad Sa-r
CK
des
sine erit 
a
Bn V aequ n
Porro ob triangula similia  BFC. BGA
erit AB ad AG, ut CB ad CF
m
ergo erit v aequ. bd. quam aequationem
n
(3) san
et duos vnlores aequando fiet: mn aequ L
Rursus ob eadem triangula similia
et fat: _
(12Magu. + s2 + Er+2q S9e r (4) eb t rrgg2 r
ext Porro X +Z aequ. m. quanquam 2 aequ + s. .. . . . . 14) s..
signa variari possint, prout G cadit intra et scribendo per compendium ent
B et C. vel extra in alterntium latus, quod An aqu + O ()) et An aequ +0 (+) D
tamen ut mox patebit nullam producit facile pater fore n faciendoque +0 + D aequ e.
in calculo varietalem. et quia an su itemque +0- 8 aqu 4. patet fore
ob Trianguela rectangula erit:  vel m aequ. +O, et n aqu + D
ab d’ aequ. b= x et b d’ aequ  = fE) tn qu +D aetite aequ +
(5) i
n
6
Ergo  aequendo duos valores fiet: L
Ln’aequ 4 7t sive per At
fiet  us b- n aqu X - Zm 
vel ma aequ O ed et n aequ = D
vel m aequ= 3 et n aequ = O
adeoque aequatio, quatuor, quidem
vel B X. Z aequ. b- p. Unde jungendo aequationes
LSI
4 et 9 sibi invicem addendo et a se invicem,
Subtrahendo fiet 2X aequ.
(1C)
b+r
+ m+ bnu
M a (12) p b2p
et 2Z aequ. +m + m Sive Zaequ.
quem valorem aequando valori ex aegu. 1.
em
fiet; m +n-== mn aqu. b unde ab aequ. 3.
(14)
fiet: in +n -2cmh + 2= mn + Emn aequ. b7 Ers4. 1
sive man Aq sgrni 
e
Si
m- n aequ
(4) S b afi s qu bd
quia nihil refert quaenam sit
longitudo ipsis 4. modo ratio qd
rad 4. sit data, faciamus ququ.bd
et fiet
i qe habebit radices sed tamen non
nisi unicum eris triangulum quod
satis faciet quaestibni, permutatis
tantum laterum significationibus
itemque sumendo ab utraque baseos
parte. Quatuor itnque Triangula super
satisfacientia quaestioni super eadem
basi positione data collocari
possunt omnique con
a inter se
BdE DABH
AB. C. (AB