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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 29r, page id 00068196:0057
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cF. GBerit F ut pri
 HBm: 1
d
P. 68B. 1.  -5 h
D.
D. 08
sit punctum C relatum adiangulum in A rectum per coordinatas CB, C(3
et idem relatum ad alium angulum in E rectum, perer ordinatas CF, C. desideratur
valor coordinatarum posteriorum ex prioribus. Refeatur ipsum punctum E, referendi
ipsum angulum rectum priorem per coordinatas EG, EY.. determinetur et angulus
rectus posterior, dum ade detem dato puncto H, quo alterutrum hujus
posterioristatus anguli latus  se cat alterutrum prioris AB. Quaeruntur jam i eF
 EF FC, ex ipsis CB, CB, E. V, EG. Hic modus est utilis, quando punctum A, cum
celi tangule angulo suo est primarium, et constans, punctum vero E
secundarium eevacum suo angulo et variabile. Alioqui si ambo puncta A et E
Aet E, amboque anguli recti pari jure  aterentur, praestaret tractari etiam eodem
modo, quod fieret  jungendo rectam AE, cujus angulis ad latera rectorum
producatur CB dum ipsi F H occuroat in K
angulorum omnia determinarentur
cit KFC V EGH CTK N HGC et producatur CB, dum ipsi FH occurrat in X
jam sint HGi GEoEH = M: M: A
eetq e ecat et rursus HBK V AGE. ent KB = HBM: m
eR et KC = BC + HBn: m et P = (BC + HBm:m) m: h
adeoque  CF = CB(mJh + HBN: h est autem HB= AB CB - E DS BAH, et
erit CFK  HGE
eFC C CBmCh = CBMhC E M ih m:h vel CF- C. Bmh CBm: h + Cβn: h = A HN: h
H et FH = FK  R H. est autem FK ad KC seu ad
et R H = HBh: m
FB F HBN: m ut M ad h et fet FH - CBn: h + HBn: mh ergo fit
s seu CBa: A + HB(ex -ha ) nh
D C vel EF EH
FH = C Bn: h + HBA: inh  HBh: M
pari modo CE ut inveniamus  consi sit q punctam quo CB secat ipsam E, et
in FH = CBn: s + CB (nin thi): mhi AH serm- hh): nsi
FβQ = Rβp: M et R(S - AB - Ak
adeoque Cg = Cβ, = Aβp: m + ARn : m et (∞ = Cβm: h = AB p: h + ARM: h
CF = CB mih + CB(n: h = AHC: h
CQ = lCβ= B2
fiet C9 = Cq m: h
vidganais ne licea ubi patet puca variare signa pro sita punctorum.
Prorsus uti habuimus
indeamus an liceat obfinere expressionem in qua non varient signa
rectarum ER, EH, dantur
8. 0 ab +AB. B sane datis punctis A et si, datisque angalis
varietatem signorum, atque obtinere aliquid
E. 16, 18 = 15 - 1 2 punctum E, et angulus reclus ad E
EF = ABn-HG- AB  i sed videamus an liceat tollere
GBe quae memona
et CB = EG+V(
E no. AP- 1  comnis expressionem prorsus versatem
RV = E) m: M et ARM: h = EGp : h = E) m: h et proinde
CB = E9) + GB
facilius possit vetineri
fiet C8 = (Epm: h) + GBm: h (= EGn: h, - ) 3m:h (+ EG m B = 2) m: h), ee
simisiter AH = AG+ GH
AR, = EG - R)
adeoqueemum C_ GBm: h - Y 3M: h
et GH = EGm: p adeoque AH =  + 2G m:  et A H(n: h = AGM: h + EGm: h
et fiet CF = (EG m: h) + Vβm: h (+ EV B: h) + GBn: h (= EV: h) C EGm: h)
in pemper afectat signo
neme , , B C, sism est-
Habemus ergo
CD = GBm: h - VBp: h
CF = GBn: h + VBm: h
ubi patet CF quedeses in cujus valore sunt signa +, cadere intra CB et C
eadem quoque si licebit
tanc conclusionem sic licuisset consequi sine calculo
Erit utique
raesas prosequioribus
pohibui aute
Cβ secet EG in F, et ex H in ED agatur normalis Hd
EAdE, erit Ed = Ex M: h = V Bm: h
erita   = CH n: h = GBn: h
GBn: h + VBm: h
 ab triangula similia ed es tiam uli simili
agatur et ex i Fremus a liainguta simulia HGE, A L, CGd
similiter, ob eadem triangua similia eri  S = Ex n: h seu gB3n: h, et CD- CH m: h
adeo jam cF = Ed + d8, ergo EG= C
uncta A, R, V B, non ingrediuntur calculum ideo potuissent omitti sofficunt enim G, E
ad ang. rect. EGB.) et rarsus
et denique rectanus. 55 na Rreferendon
esse adhiberi
sed = CD = 1S ergo C4 = GBm: h - VBn: h
ufticit compleri rectangulam GBCH, EEFe (refeunto
et rectangulum E FC8(referendo C ad angulum rectum FE,
Brevius adhuc amisso pun video, non opus
erinit
EM n. h
punctum G, sed pro recta GB, ectam E p fit cB= Eomit-
ad angulum rectum FC8)
mulita recti ad idem punctum nempe pEH et FED: Datur relatio puncti C ad priorem, quaeritur relatio ejundem
es verie osenem
pront quidem
Datur et auto quem ans si rest
min,h, CF seu E =  + 59. (8 )E0 = EF m
i u es andnte mt i
aut extra E ut  et velato ad
in vedum bero let proviae et poesplitur auta ut leti t est
quidem E9 pro valore ipsius E8,1
gelurrecta no in Eg hatur
sed siangulius rectus dactas
ara nelatio non
us stat ad pon
 pG AB malea
ritque Ep = AB - A
A EA = AB- A7