Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page 12
... Triangle ( ABC ) . C A B a 3 post . b 1 poft . C15 def . d I ax . e 23 def . b 3 * About the Centers A and B , with the com- mon distance AB or BA , describe two Circles cutting each other in the Point C ; from which draw two right ...
... Triangle ( ABC ) . C A B a 3 post . b 1 poft . C15 def . d I ax . e 23 def . b 3 * About the Centers A and B , with the com- mon distance AB or BA , describe two Circles cutting each other in the Point C ; from which draw two right ...
Page 15
... Triangles BAC , bac , and the An- gles B , b , as alfo the Angles C , c , do agree , or coincide , and are equal . Which was to be demon- Strated . B D e A PROP . V. C The Angles ( ABC , ACB ) at the Bafe of an Ifofceles Triangle are ...
... Triangles BAC , bac , and the An- gles B , b , as alfo the Angles C , c , do agree , or coincide , and are equal . Which was to be demon- Strated . B D e A PROP . V. C The Angles ( ABC , ACB ) at the Bafe of an Ifofceles Triangle are ...
Page 16
... ABC ACB . Q. E. D. fore . h 3 ax . a 3 I. bi post . c 2 byp d 1 byp . e 4. I. f9 ax . • COROLLART Hence , every equilateral Triangle is alfo e- quiangular . B D A PROP . VI . · C If two Angles ( ABC , ACB ) of a Triangle ( ABC ) be ...
... ABC ACB . Q. E. D. fore . h 3 ax . a 3 I. bi post . c 2 byp d 1 byp . e 4. I. f9 ax . • COROLLART Hence , every equilateral Triangle is alfo e- quiangular . B D A PROP . VI . · C If two Angles ( ABC , ACB ) of a Triangle ( ABC ) be ...
Page 19
... ABC ; and b bife the B Angle C , by the right Line CD : which Line fhall alfo bifect the given Line AB . C For AC BC ... Triangle : and draw the Line FC ; and it will be the Perpendicular required . a I. I. c conftr . d 4.1 . e 3.1 . f I. I. ...
... ABC ; and b bife the B Angle C , by the right Line CD : which Line fhall alfo bifect the given Line AB . C For AC BC ... Triangle : and draw the Line FC ; and it will be the Perpendicular required . a I. I. c conftr . d 4.1 . e 3.1 . f I. I. ...
Page 22
... ABC . m 13. 1 . n 16. I. o 4 ax . B PRO P. XVII . A с O Any two Angles of a Triangle ( ABC ) taken together , are lefs than two right Angles . D Continue out the Side BC . Now because the Ang . m ACD + ACB two right Angles , and the Ang ...
... ABC . m 13. 1 . n 16. I. o 4 ax . B PRO P. XVII . A с O Any two Angles of a Triangle ( ABC ) taken together , are lefs than two right Angles . D Continue out the Side BC . Now because the Ang . m ACD + ACB two right Angles , and the Ang ...
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.