Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page 164
... Polyhedron is a Solid of many Sides or Faces . PROP . I. BT D A E One part AC of a Right Line cannot be in a Plane , and another part CB with- out the fame . Continue out AC in the Plane to F ; then if CB be in the fame ftreight Line ...
... Polyhedron is a Solid of many Sides or Faces . PROP . I. BT D A E One part AC of a Right Line cannot be in a Plane , and another part CB with- out the fame . Continue out AC in the Plane to F ; then if CB be in the fame ftreight Line ...
Page 213
... Polyhedron BOPRXYTSK in BCDE the greater of two Spheres , having the fame Centre A , which shall not touch the Superficies of the leffer Sphere FGH . 3 . Cut the Spheres by a Plane paffing thro ' the Centre A , and the Sections will be ...
... Polyhedron BOPRXYTSK in BCDE the greater of two Spheres , having the fame Centre A , which shall not touch the Superficies of the leffer Sphere FGH . 3 . Cut the Spheres by a Plane paffing thro ' the Centre A , and the Sections will be ...
Page 215
... Polyhedron within the Arches BX , KX , compofed of Pyramids , whofe Bafes are the Quadrilateral Figures KBOS , SOPT , TPRY , and the Triangle YRX , and Vertices at the Point A ; and if there be made the fame Conftruction on each of the ...
... Polyhedron within the Arches BX , KX , compofed of Pyramids , whofe Bafes are the Quadrilateral Figures KBOS , SOPT , TPRY , and the Triangle YRX , and Vertices at the Point A ; and if there be made the fame Conftruction on each of the ...
Page 216
... Polyhedron , and AG to the Superficies . Therefore the Superficies BOSK does not touch the Superficies of the leffer Sphere ; and the fame may be demonstra ted of the other Planes of the Polyhedron . Q. E. D. COROL Alfo if a folid ...
... Polyhedron , and AG to the Superficies . Therefore the Superficies BOSK does not touch the Superficies of the leffer Sphere ; and the fame may be demonstra ted of the other Planes of the Polyhedron . Q. E. D. COROL Alfo if a folid ...
Page 217
... Polyhedron , which is in the Sphere defcribed about the Center A , to the whole folid Polyhe- dron that is in the other Sphere , hath a triplicate Proportion of that which AB hath to the Line drawn from the Center of the other Sphere ...
... Polyhedron , which is in the Sphere defcribed about the Center A , to the whole folid Polyhe- dron that is in the other Sphere , hath a triplicate Proportion of that which AB hath to the Line drawn from the Center of the other Sphere ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.