Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Page 10
... the fame Space . 9. Every Whole is greater than its Part . 10. Two right Lines cannot have one and the fame Segment ( or Part ) common to them both . 11. Two 11. Two right Lines meeting in the fame Point , ΤΟ EUCLID'S Elements .
... the fame Space . 9. Every Whole is greater than its Part . 10. Two right Lines cannot have one and the fame Segment ( or Part ) common to them both . 11. Two 11. Two right Lines meeting in the fame Point , ΤΟ EUCLID'S Elements .
Page 15
... common : therefore fhall the Angle ABE be ACD , and the e . Angle AEB ADC , and the Bafe BEDC . Allo EC is DB . Whence in the Triangles f 3 ax . BCE , BDC , the Angle ECB fhall be = DBC , ( which is the latter part of the Propofition to ...
... common : therefore fhall the Angle ABE be ACD , and the e . Angle AEB ADC , and the Bafe BEDC . Allo EC is DB . Whence in the Triangles f 3 ax . BCE , BDC , the Angle ECB fhall be = DBC , ( which is the latter part of the Propofition to ...
Page 16
... common ; and the An- gle DBCa ACB , the Triangles DBC and ABC fhall be equal to each other ; and fo the Part is equal to the Whole : which is fabfurd . = с CORO L. Hence every equiangular Triangle is alfo e- quilateral . PROP . VII . If ...
... common ; and the An- gle DBCa ACB , the Triangles DBC and ABC fhall be equal to each other ; and fo the Part is equal to the Whole : which is fabfurd . = с CORO L. Hence every equiangular Triangle is alfo e- quilateral . PROP . VII . If ...
Page 18
... common , and the Bafe k DF - FE : therefore the Angle DAF EAF . Q. E. F. Hence appears COROL . the way of dividing an Angle into thefe equal Parts , viz . 4 , 8 , 16 , & c . which is done by a new bifecting of each of the for- mer ones ...
... common , and the Bafe k DF - FE : therefore the Angle DAF EAF . Q. E. F. Hence appears COROL . the way of dividing an Angle into thefe equal Parts , viz . 4 , 8 , 16 , & c . which is done by a new bifecting of each of the for- mer ones ...
Page 19
... common , and DF = EF ( by Conft . ) whence the Triangles DFC , EFC are mutually equilateral ; therefore & the SS . 1 . Angle DCF = ECF ; whence FC is a Perpen - h 10 def . dicular . Q. E. F. This and the following Problem are easily per ...
... common , and DF = EF ( by Conft . ) whence the Triangles DFC , EFC are mutually equilateral ; therefore & the SS . 1 . Angle DCF = ECF ; whence FC is a Perpen - h 10 def . dicular . Q. E. F. This and the following Problem are easily per ...
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.