Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Página 8
... Parallelogram be divided by them into four Parallelograms ; then those two Pa- rallelograms , DG and GB , thro ' which the Diameter does not pafs , are called Comple- ments ; and the other two , HE , FI , which the Diameter paffeth ...
... Parallelogram be divided by them into four Parallelograms ; then those two Pa- rallelograms , DG and GB , thro ' which the Diameter does not pafs , are called Comple- ments ; and the other two , HE , FI , which the Diameter paffeth ...
Página 34
... Parallelogram . For ( by 8. 1. ) the Ang . ABC BCD ; there- fore AB , CD are " parallel . In like manner the Ang . BCA is CBD ; therefore AC , BD " are 35 def . alfo parallel whence ABDC is a Parallelo- gram . Q. E. D. i Hence C Hence ...
... Parallelogram . For ( by 8. 1. ) the Ang . ABC BCD ; there- fore AB , CD are " parallel . In like manner the Ang . BCA is CBD ; therefore AC , BD " are 35 def . alfo parallel whence ABDC is a Parallelo- gram . Q. E. D. i Hence C Hence ...
Página 35
... Parallelogram . PROP . XXXV . Parallelograms ( BCDA , BCFE ) conftituted upon the fame Bafe BC , and between the fame Parallels AF , BC , are equal the one to the other . A D B C C a 29. I. 4. 1 . For AD BC = EF , add DE common 34. I ...
... Parallelogram . PROP . XXXV . Parallelograms ( BCDA , BCFE ) conftituted upon the fame Bafe BC , and between the fame Parallels AF , BC , are equal the one to the other . A D B C C a 29. I. 4. 1 . For AD BC = EF , add DE common 34. I ...
Página 36
... Parallelogram ABCD , be conceived to be moved perpen- dicularly along the whole Line BC , or BC along the whole Line AB , the Area of the Rectang . ABCD fhall be produced by C that Motion . Whence a Rectang . is faid to be made by the ...
... Parallelogram ABCD , be conceived to be moved perpen- dicularly along the whole Line BC , or BC along the whole Line AB , the Area of the Rectang . ABCD fhall be produced by C that Motion . Whence a Rectang . is faid to be made by the ...
Página 38
... Parallelogram ABCD , and a Tri- angle BCE , have the Same Bafe BC , and are between the Same Parallels AE , BC , #then is the Parallelo- gram ABCD the Dou- ble of the Triangle BCE . b a , b C 34. I. c 6 ax 38 EUCLID'S Elements ,
... Parallelogram ABCD , and a Tri- angle BCE , have the Same Bafe BC , and are between the Same Parallels AE , BC , #then is the Parallelo- gram ABCD the Dou- ble of the Triangle BCE . b a , b C 34. I. c 6 ax 38 EUCLID'S Elements ,
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.