Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
Results 1-5 of 51
Page 9
... right - angled Trian- gle , is equal to the two Squares of the other Sides . A Problem is fomething propofed to be done as to make a Circle pass thro ' three given Points . A Lemma is a Propofition laid down only for demonstrating fome ...
... right - angled Trian- gle , is equal to the two Squares of the other Sides . A Problem is fomething propofed to be done as to make a Circle pass thro ' three given Points . A Lemma is a Propofition laid down only for demonstrating fome ...
Page 12
... given finite right Line ( AB ) to defcribe an equilateral 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 ...
... given finite right Line ( AB ) to defcribe an equilateral 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 ...
Page 13
... given Point A , to draw a right Line AG equal to a right Line given ( BC ) . H B D F C E a с b bi C I. I. d 2 poft . About the Center C , with the Distance CB , defcribe the Circle CBE . Join AC , upon a 3 poft . which raise the ...
... given Point A , to draw a right Line AG equal to a right Line given ( BC ) . H B D F C E a с b bi C I. I. d 2 poft . About the Center C , with the Distance CB , defcribe the Circle CBE . Join AC , upon a 3 poft . which raise the ...
Page 14
... right Lines ( A and BC ) being given ; from the greater ( BC ) to take away a right Line ( BE ) , equal to the leffer ( A. ) D E B C & 2. I. b15 def . c conft . di ax . = From the Point B draw the right Line BD A ; then a Circle ...
... right Lines ( A and BC ) being given ; from the greater ( BC ) to take away a right Line ( BE ) , equal to the leffer ( A. ) D E B C & 2. I. b15 def . c conft . di ax . = From the Point B draw the right Line BD A ; then a Circle ...
Page 18
... given right - lined Angle BAC , into two equal Parts . i - Take h AD AE , and draw the Line DE , upon which make an equilateral Triangle DFE : then draw the right Line AF , and it fhall bisect the Angle BAC . · For AD AE , and the Side ...
... given right - lined Angle BAC , into two equal Parts . i - Take h AD AE , and draw the Line DE , upon which make an equilateral Triangle DFE : then draw the right Line AF , and it fhall bisect the Angle BAC . · For AD AE , and the Side ...
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.