Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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... fecond Book wants the Schemes of Prop . 5 , 6 , 7 , 8 , which by a bare Contemplation and Attention to the Text , would be almoft fufficient to evince their Truth , without reading the Demon- ftrations . Thefe Thefe Inconveniencies I ...
... fecond Book wants the Schemes of Prop . 5 , 6 , 7 , 8 , which by a bare Contemplation and Attention to the Text , would be almoft fufficient to evince their Truth , without reading the Demon- ftrations . Thefe Thefe Inconveniencies I ...
Seite 12
... fecond , the remainder of the firft fhall . be the double of the remainder of the fecond . As if A 2B , and C 2D : then fhall A - C = 2B2D . = The Citations are thus to be understood : When you meet with two Numbers in the Margin , the ...
... fecond , the remainder of the firft fhall . be the double of the remainder of the fecond . As if A 2B , and C 2D : then fhall A - C = 2B2D . = The Citations are thus to be understood : When you meet with two Numbers in the Margin , the ...
Seite 109
... fecond B , and fourth D , according to any Multiplication foever , either both together ( E and F , ) are less than G , H , or both together equal to them , or both together greater , if those Magnitudes E , G , and F , H be taken ...
... fecond B , and fourth D , according to any Multiplication foever , either both together ( E and F , ) are less than G , H , or both together equal to them , or both together greater , if those Magnitudes E , G , and F , H be taken ...
Seite 110
... fecond B , than the third C to the fourth D. C D If be it is not necessary from this De- finition that E always exceeds G , when F is iefs than H ; but that it is poffible for it to do fo . IX . Analogy at leaft confifts of three Terms ...
... fecond B , than the third C to the fourth D. C D If be it is not necessary from this De- finition that E always exceeds G , when F is iefs than H ; but that it is poffible for it to do fo . IX . Analogy at leaft confifts of three Terms ...
Seite 111
... fame Proportion ; and it fhall be in the first Order of Magnitudes , as the firft is to the laft , fo in the fecond Order of Magnitudes is the first first to the last or otherwise it is the Compari- Book IV . EUCLID'S Elements . III.
... fame Proportion ; and it fhall be in the first Order of Magnitudes , as the firft is to the laft , fo in the fecond Order of Magnitudes is the first first to the last or otherwise it is the Compari- Book IV . EUCLID'S Elements . III.
Häufige Begriffe und Wortgruppen
9 ax ABCD abfurd alfo alſo Altitude Angle ABC Bafe BC Baſe becauſe bifect Center Circ Cone confequently conft COROL Cylinder defcribed demonftrated Diameter draw the right drawn EFGH equal Angles equiangular equilateral Equimultiples EUCLID's ELEMENTS faid fame Multiple fecond fhall fimilar fince firft folid fome fore four right ftanding given right Line gles Gnomon greater Hence infcribe leffer lefs likewife Line CD Magnitudes manifeft manner Number oppofite Paral parallel Parallelepip Parallelepipedons Parallelogram perpend perpendicular poffible Point Polyhedron Prifms Probl PROP Propofition Pyramids Ratio Rectangle right Angles right Line AB right Line AC right-lined Figure SCHOL SCHOLIU Segment ſhall Side BC Sphere Square thefe thofe thro tiple Triangle ABC Whence whofe whole
Beliebte Passagen
Seite 31 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 145 - Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Seite 33 - ABD, is equal* to two right angles, «13. 1. therefore all the interior, together with all the exterior angles of the figure, are equal to twice as many right angles as there are sides of the figure; that is, by the foregoing corollary, they are equal to all the interior angles of the figure, together with four right angles; therefore all the exterior angles are equal to four right angles.
Seite 27 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Seite 31 - The three angles of any triangle taken together are equal to the three angles of any other triangle taken together. From whence it follows, 2.
Seite 11 - That a straight line may be drawn from any point to any other point. 2. That a straight line may be produced to any length in a straight line.