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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 11
# Folio 18v, page id 00067970:0036
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nde statum habetur tam m. quam n.
sed ut constructio fiat commodor, ponamus
q aequ. Sbd. seu g aequ bd, id est
quaeratur media proportionalis inter AB. BD.
quae vocetur q. nihil venim refert qualis
sit q. modo rati ipsius. r ad 9. sit data
Get Y. in una ponantur recta HTS P.
ita ut HS sit 4.  et S t r.
itemque sT erit H, q. r. et HP, erit qus 9+r
quod clrius
quod clarius patet rudi exemplo in numeris;
sit b basis aequ. 14. altiludo d aequ 62
erit q seu sbd aequ. circiter 92. et rsit 22
fiet Squ-r aequ. 9. 2r + 29 aequ. 233
2r+ 29 Fa. Y. sit 13. et rrcaequ1
-
aequ 14 se
2r- 29 aequ = 13 3
1217
Er.29 x 192. r aequ 123
et fo aequ. 1. . . . . . . . . aequ 11. Ser. (123
mn seu T6 + 2r4 29Sq r aequ + 20L
man seu Yb + er - 29 Sq 1u 8qu (+) 8
mom
 equl  Hinc jam
si  sit + et (4) sit + erit M aequ 14 2 n aequ6.
+ + (+) - m 6 n 142
- (+) = m -14  n -6
= (+) + m -6 n -14 2
Constructio ipsa ita absolvetur
positis in directum AB basi et Bd quae altiludini
sit aequalis circa
 Basi AD producta in D ut sit Bd aequalis altitudini
describatur semicirculus circa ABd cujus peripheriae ex B. erecta d angulos rectos Bq
erect perpe occurrat in g. Erit BG. p. aiqu sbd
ponatur jam angulo ad verticem   ess datus esse aequalis BER et ex B
est in 4R demittatur perpendicularis BR, eut A9, r.. sit recta in quia
hoc ordine designeatur puncta p_VEW. sitque PH aego HH aego q vi
et HE aequ 9- r. Circa diametium DE describatur semiciicumferentia cui ex
H normaliter erecta occurrat Ha quae erit r seu media proportionalis
inter PH, (seu 9+Y) et HE (seu q- Y). Porro recta IVP productitur.
versus ultra p usque ad β, ut fiat PB aequ Ha seu  q- r. Et cum
ex constructione sint PHaego 9+r. et HE aequ 9- r, erit DE aeqo qud
unde detrahatur E) aequ 2Y. restabit pD aego 29-27. Jam
rectis BY. et β1B velit diametris imponantur ad easdem partes semicircum
inferentiae BDY. BS BSW. quae secabunt rectam pB d ex P nonmaliter eductam
in spunctis D et. d. erit pB med prop. inter B, seu fatur et p) seu 29. et
id est eut pB aequ Y E9- ir Sq - 1 et similiter erit pd media prop. inter Cpseurro
et pV seu 29+ 2r id est erit pd aequ. SEgtrsq . jam ipsa pd transferatur in BA
sumtam in BQ si opus producta jungaturque AX, quae erit VIV +29+ErSq aequ. m +n.
ee H
circa  ejus mne d cujus punctum medium sit
Raru Dasi AB velut diametio imponatur femicircumferentia A B. et ejus arcui AC
similitem
subtendatur recta Ass aequalis ipsi pB. jungatur De quae ent (+Er -qq  a mun. Hujus parti
cusque dimidiae sumantur in ot aequale Y eo versus = A, et HE ver l D unitque AE aequ in vel 1 et ACo aequ. n. vel contra,
et Acd aqu n vel _ habentulu latera Tianguli quaesita n seu BC et n seu AC. Quod faciendum er ab