Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page
... because the Learner's Atten- tion to the Propofition he is reading , will be interrupted not only by constantly taking his Eye off from the place he is reading , to view the Scheme , which will always be too diftant , let the Cuts fold ...
... because the Learner's Atten- tion to the Propofition he is reading , will be interrupted not only by constantly taking his Eye off from the place he is reading , to view the Scheme , which will always be too diftant , let the Cuts fold ...
Page 2
... because the Point defcribing it is of fome Bignefs . 3. The Bounds of a Line are Points , as the Points A , B. 4. A Right Line is that which lies evenly be- tween its Points . 5. A Superficies is that which has only Length and Breadth ...
... because the Point defcribing it is of fome Bignefs . 3. The Bounds of a Line are Points , as the Points A , B. 4. A Right Line is that which lies evenly be- tween its Points . 5. A Superficies is that which has only Length and Breadth ...
Page 3
... example , the Angle DAF is greater than the Angle CAB ; tho ' the Lines or Sides AD , AF of the one are less than the Sides AC , AB of the other because F B B 2 they they do not incline or bow fo much to one Book I. Definitions .
... example , the Angle DAF is greater than the Angle CAB ; tho ' the Lines or Sides AD , AF of the one are less than the Sides AC , AB of the other because F B B 2 they they do not incline or bow fo much to one Book I. Definitions .
Page 15
... because ab AB alfo the right Line ac fhall fall up- on AC , because the Angle Aa ; moreover , a hyp . the Point ofhall fall upon the Point C , because AC ac . Therefore the right Lines bc , BC , because they have the fame Bounds , fhall ...
... because ab AB alfo the right Line ac fhall fall up- on AC , because the Angle Aa ; moreover , a hyp . the Point ofhall fall upon the Point C , because AC ac . Therefore the right Lines bc , BC , because they have the fame Bounds , fhall ...
Page 16
... because BD = CA , and the Side BC is 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 ...
... because BD = CA , and the Side BC is 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 ...
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.