Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 273r
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.74.
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The machine reads it as
- problema:
- Data trianguli basi altitudine, et summa 2 vel intoloendo in factores incognilorum latus.
- laterum invenire Triangulum:
- _ Basis AB = a (9)
- 2. Altitudo DC = b (37
- 3. Summa Laterum AC + CE = c 1E
- 4 Latus minus AC (3 j = y vide = (9)
- SLatus majus CBC (37 y + X. vide = (12))
- 6. Ergo summa laterum c = 2y+X (X = Y, 2ab- ac- a+
- 7. Item (per 3-5= 4) y = C - y - X.
- 8 Brgo addendo utrobique y 1) 2y = C.X
- controhere in proclivi est Cx
- 9. Et (Et divitendo per 2. y = C- X fatus Minu AC. sufficit interea inventam aequationem.
- 10. Ergo sulsituendo pro G m (5) pro y. ejus = ex9)
- 3t X = c- X 4K
- 11. Jungeado denominatores: y + X = C- x + 2X
- M. abseiendo X inama qqua tionis parte, superflue scriptum 44
- 7+x = C+ x= Latus Mapes BC
- 13. differenlia laterum BE = X. (2)
- C
- Hinc apparet sufficere ex terminis incognitis) ex -ax - 2cxa b a + Cg - 2ca )R9
- inveniri X. Quod ita quaeremus: e
- 56 Y, 1X 2a-. -1 - v 800
- a91 _ (9) C+ x = 2CX (9) (256
- B. (a)- BB (2) =(11
- 6400 255 + 44- 216, 220 40
- 16. fungendo denomeratores c2+ 25t 141
- 286
- 16. R9(5) = AD. (7 6400(100 25.
- 17 (1 - (16) = a - R9 (15) = DB. H)
- 18 467) = a + (15.) = 2akg (5) C y= DB. Lr
- ere
- 19 (et ) = a+ C+X 2Cx 1 . -bC.
- 20 se taljiciatur et +b, litur sinpli
- 21 ex taur 1dine Dermi t 44 fiet, quod
- notitam est litura dupbici
- 23. Hire gtur (19) (+ BCl eteris majoris =
- 23. Scribatur plene aequatio (1) (12) c
- a Cart c ag5 +X 2C= C+ X+ 244,
- 1564 t mmi
- Cxx . 2e- b, + - HBC.)
- (20 Poliatur abjiciendo = b et +b litura simplici R9 64 = 8
- 21. Jungendo iNices unum denominatorem
- 22. extrahendo, Radicem ex A4. denominatore4.
- 23. prit equati 2)
- -32 100
- Aa + C +X. 2CY ∞ - fa RA C + X = 2 er. 4b = C + f + ECx p257
- 2.
- (2
- 640f
- 24 Ponatur in uno latere sola Rq. utrumque dividatur per a ft et multiplicetur per
- Anqc Al acX 448, Ca par 2CaC
- = A9C +X = 2CX - 4b = X+ 2CX- 4a- N + 2CX- 4 cx- 4c
- 25. Poiatur aequatio auferendo superflua c litura. X litura dupliciss. jungendi
- duo 2CX et ultiplicando utrumque fractionis terminum per 4, liturasse
- 26. Quadretur utrumque latue, fiet: 15625b
- 512
- =C X + 2CX + 4bV = Cx + a - 2Ca X
- 27. Multiplicetur ogapia per a fiet
- aC
- a
- 1029
- a -4cKeK + XX =
- a. X + 2CaZ + 44b =CX + a XaX 1o17
- 28 junguatim similes incogniti potestates solae, fut ut se.
- e elui tallant pro 4ca X subsituendo oeax
- (768)4+ C X - 4Ca = - ac- aX + 4a b = X 1024 6+ 5X
- ac ax +4ab a4
- 24 Ergo dividendo utrumque pe e 4C erit. X - X
- imaentur duo similes incogniti Restates: C X + a X a. Aca X X 4a b
- equuraidanti p C + a f et X ∞ at 4ca x + a +ab X+4 ca atq a 4a b nin
- a.
- Xetax
- ax = 44 b. ac = d
- 30. dividantur omnia per C + a. ut X liberatur, fiet.
- S compleatur H. fiet: 1t 18
- X+Ca
- E4
- 32. Extahatur rad fiet+
- X.
- 162
- 2
- - ....
- 2C4
- 2+ a 12 ca
- 22. Engo habemus aequationem hani quaesil
- a
- 2
- rea. Quod in breviorem formam
- s
- ta CX 2C, Mplic pe
- Cta X X, Ha X X
- e
- (XV= a
- 102a(64 X
- 10 u 1os
- 44
- 220
- +CX - x = cu 2 CX 14
- k
- =X = RGZCX
- = X = 2CX + 4
- CX Y aX
- asc
- 44+25
- rintisqu
- 255+
- 1029
- 70
- sh
- 356-227
- eaie
- 5X + X= 4b+ +CX C- a
- X+ ab + X C a
- fa
- in
- 29 7024
- a
- ib
- 6400
- X ACX= 4 Cx c. a iorg
- ac la 45 at 108.
- si
- id
- 2
- ACX = 2CX 4 46 - cX
- s
- 2
- ieat
- 3s3
- 10r4
- e
- 13
- 256] 128164
- 100 50 l25
- t 36, 1
- eta
- netax
- perax
Cite
Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 273r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0545?run=74