Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page 3
... touch one another ; yet not fo that both of them be in the Same Direction : as ' A BC . C SCHOLIUM An Angle is faid to be fo much the lefs , the nearer the Lines that make it are to one ano- B A A ther . Take two Lines AB , BC , touching ...
... touch one another ; yet not fo that both of them be in the Same Direction : as ' A BC . C SCHOLIUM An Angle is faid to be fo much the lefs , the nearer the Lines that make it are to one ano- B A A ther . Take two Lines AB , BC , touching ...
Page 61
... touch each other , when they meet each other , fo as not to cut one another . The Circle BFG cuts the Circle FGH . A D E B G C F H F A K B G H J N D E L C pendicular ( GI ) falls . 4. Right Lines FE , KL , in a Circle GABD , are faid to ...
... touch each other , when they meet each other , fo as not to cut one another . The Circle BFG cuts the Circle FGH . A D E B G C F H F A K B G H J N D E L C pendicular ( GI ) falls . 4. Right Lines FE , KL , in a Circle GABD , are faid to ...
Page 66
... touch one another , ( in B ) they have not one and the fame Center F. For if they have , right Lines FB , FDA being drawn , then would FD = FB f abfurd FA , which is e PROP . CA PRO P. VII . D G E H B 66 . EUCLID'S Elements .
... touch one another , ( in B ) they have not one and the fame Center F. For if they have , right Lines FB , FDA being drawn , then would FD = FB f abfurd FA , which is e PROP . CA PRO P. VII . D G E H B 66 . EUCLID'S Elements .
Page 70
... touch one another on the outfide , the Line AB , which joins their Centers , A , B , Shall pass thro ' the Point of Contact C. A B DE d 20. I. 9 ax . If poffible let ADEB be a right Line cutting the Circles ; not in the Point of Contact ...
... touch one another on the outfide , the Line AB , which joins their Centers , A , B , Shall pass thro ' the Point of Contact C. A B DE d 20. I. 9 ax . If poffible let ADEB be a right Line cutting the Circles ; not in the Point of Contact ...
Page 71
Euclid. PROP . XIII . One Circle BACD cannot touch another BZDE , in more Points than one , whether inwardly or outward- ly . E H .B D 2 K For if poffible let the one touch the other in two Points as B , D. a h And take the Centers H , O ...
Euclid. PROP . XIII . One Circle BACD cannot touch another BZDE , in more Points than one , whether inwardly or outward- ly . E H .B D 2 K For if poffible let the one touch the other in two Points as B , D. a h And take the Centers H , O ...
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.