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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
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De Geodaesia.
CAP. 24
de latieudo xstimanda erie non ex linea urcungi crantrersim du
eta (ica enim lacicudo eslet plane incerca, e modo major modo
minor dicenda, prouc illius cranlversae linee ad arbicriu Cumpea
minor majorre tuerie obliguitas) Ced ex linea directe live per-
Pendicularicer cranscunce; puca non ex linea inclinata DC vel
BC, sed BF vel DH. Ec quidem E suxponatur aserculus, un
illa Forma consticurus, longicudinem habere DB quantam-
cunq; ejus lacicudo non estimanda eric (ne quidem ulu com-
muni) quanta est DO, led quanca cABF, aliare ejulmodire.
cta perpendiculariter ducta. Oux quidem ue cranscuneium
omnium est brerissima, ita Cola cerra eAt; cum quae oblique
transcune, pro rariaca obliquirace, variane eriam longicudi
nem.
Rcq; haec de magnieudine parallelogrammi dixisse lufficiat.
Nempe, si Poralleloerammum comparare libeat (non praecise ad quadra
tum, sed) ad Duadrangulum aequilarerum, (sive quadratum fuerit sive
Rhombus, quod exposito Paralleloerammo sit aeguianeulum, hoc est,
Pariter inclinatum; ducenda sunt invicem duo latera ad eundem quemlibet
anculum constitura: Si vero Paralleloerammum, urcunque inclinatum, ad
solum Duadrarum comparare placeat; ducendum est latus quodvis in ren
etam ab eo latere ad latus opposirum perpendiculariter ductam. Oui qui
dem duo rectarum invicem ductue, in Parallelogrammo Re-
ctangulo, cancundem ralent; in Obliquansulo, non icem.
Quae aurem de Mulriplicatione jam dicta sunt, es de Divisione (mu
ratis mutandis) intellipenda sunt. Ouixpe quod Muiriplicarione confi
citur, id Divisione dissolvitur. Ic ipicur ex dacis lonsicudine et
lacicudine, (sire in Parallelogrammo rectangulo, sve obli
quangulo,) habetur area mulciplicando: sC ex data area cum
lonpicudine, habetur lacicudo; vel ex dara area cum lacitudi-
ne habecur lonsicudo, diridendo. Acq; de Parallelogrammis
HactenuS.
Cum aucem Geodxesiam jam sim aggressus, hoc est, menlu
racionem Planorum; operae precium eric etiam alia brevicer
accexere quX co spectane, uc tocum illud plana menturandi ne-
socium, lalcem prouc praelentis insticuri rario postulac, ab10l-
ram. Illud vero, quancum Cuperest, mensuratione Trianguls
Fere cocum perticieur.
PH aurem Triangulum (incellige freuram planam tribus rectis ter-
minatam) vel Rectanenlum, cujus alter anculus est rectus (nars plu-
e
Mensuratio
Trianeu.