Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Seite 10
... half of the one and the fame thing , or of equal things , are equal the one to the other ; conceive the fame of things . that are the one third , one fourth of the fame thing . As if AB , and C = B : then fhall AC . 8. Things which ...
... half of the one and the fame thing , or of equal things , are equal the one to the other ; conceive the fame of things . that are the one third , one fourth of the fame thing . As if AB , and C = B : then fhall AC . 8. Things which ...
Seite 32
... half a right Angle . 5. An Angle of an equilateral Triangle is two thirds of a right Angle : for of two right Angles is equal to of one . SCHOLIU M. By the help of this Propofition , you may know how many right Angles the inward and ...
... half a right Angle . 5. An Angle of an equilateral Triangle is two thirds of a right Angle : for of two right Angles is equal to of one . SCHOLIU M. By the help of this Propofition , you may know how many right Angles the inward and ...
Seite 39
... half the Altitude into the Bafe , or half the Bafe into the Altitude : as fuppofe the Bafe BC be 8 , and the Altitude 7 , there the Area . of the Triang . BCE is 28 . PROP . A F G XLII . B E C To conftitute , or make , a Pa- rallelogram ...
... half the Altitude into the Bafe , or half the Bafe into the Altitude : as fuppofe the Bafe BC be 8 , and the Altitude 7 , there the Area . of the Triang . BCE is 28 . PROP . A F G XLII . B E C To conftitute , or make , a Pa- rallelogram ...
Seite 50
... half a right one ; therefore HE HG EFAC ; therefore HF is the 29 def.1 . Square of the right Line AC . In like manner , CI is CB2 ; therefore AG , GD , are the Rec- angles under ACCB , which are equal . Whence the whole Square ADAC2 + ...
... half a right one ; therefore HE HG EFAC ; therefore HF is the 29 def.1 . Square of the right Line AC . In like manner , CI is CB2 ; therefore AG , GD , are the Rec- angles under ACCB , which are equal . Whence the whole Square ADAC2 + ...
Seite 51
... Half - Line . We are to prove that AD x BD + CD ' = CB ' b b 31. I. Upon BC defcribe the Square CF , and 246. 1 . draw the Diagonal EB ; and thro ' D draw DHG parallel to BF , and thro ' H , KLO pa- rallel to CB ; and thro ' A , the ...
... Half - Line . We are to prove that AD x BD + CD ' = CB ' b b 31. I. Upon BC defcribe the Square CF , and 246. 1 . draw the Diagonal EB ; and thro ' D draw DHG parallel to BF , and thro ' H , KLO pa- rallel to CB ; and thro ' A , the ...
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.