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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)
# Folio 210, page id 826603459:0256
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FiC. pa8.
flatel.
De Ceodaest _.
C AP. 24.
esse pedes quauratos, aut quidem totidem quadratis pedibus aegualia, uIut
quaruor lineis pedalibus terminentur sineula. Rhembi nempe lunt
non quadraca, proxcer obliquicatem ansulorum, cum quadra-
ea omnia (ex detinitione, line rectangula. Sed ee quadraris mi-
nora lune, propter eandem obliquitatem: quod iplum evenic in
aliis parallelogcammis omnibus, sive aequilacera Hnc, sire inse-
quilatera, hoc est, sire Sinc Rhombi sive Rhombidea; minora
nempe lunt quam si essene rectansula, quamris iildem lincister-
minata. Ouod sic demonstro Geomerrice: (quippe cum de
Lolosicu agitur, qui ad Ceometriam peculiaricer accinet, de
monstracio prichmecica rix locum habec.)
Sic parallelogrammum Rectangulum AB, eiq. iloperime
erum Obliquangulum DC, ica ut lacus DB Ec ucriq; com
mune, _ DC ip(DA aequale, (reliquaq; lacera sibi opposcis
parallela _ aequalia.) enamvis aucem latera BC, DO; paral-
lelogrammi obliquangulis Cine sigillacim
aequalia laceribus BF, DA, parallelo-
srammi Rectanguli, (e reliqua reli
quis;) est camen iplum parallelogram.
mum oObliquansulum DC, minus Re-
ctansulo AB, Xquale quippe Rectangu
I0 TIB. Producatur enim lacuS C (194
H: ericq; OHI == F HI, Cguia cam C G quam F H aequancurip
A BB, Oppolico laceri in ucroq; parallelogrammo; ec, eadem
ratione, HD = FB, eDC == BC, (sedet angali ad B, C,P,
aequales angulis ad D, C, H,) aequale ele igicur criangulum
DIO, crionsulo BFC, (eiq; congruit;) quorum priori (i ad
dacur commune legmencum BDOF. hc parallelogrammum
rectangulum HB; lin posteriori, fic obliquansulum C D,
quod isicur ipsi HB ae quale cst, _ ProDterca minus quam AB,
quod erac demonstrandum. Ec similicee procederet demon-
Eracio in parallelorrammo quoris obliguangulo.
Pacerisieur 12 Phombos Parallelogrammi provosici Ob-
liquansuli AB, minores esse cocidem ouadracis Rectansul,
CD, uruc cam haec quam illi quacernis liveis pedalibus cermi.
RenEUF.
Si quaeratur intuper, quid impediat quo minus mentaras ex-
primere liceat per Rihombooxque ac duadrata. ? Respondeo,
Magnicudines explicandas ese per memluras certas, (lecus e.
nin
2