Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page 4
... meet , which is called the angular Point . As the Angle DAF fhews the Angle formed by the two Lines or Sides DA , AF ; it being the angular Point wherein the Sides meet . Moreover , right - lined Angles are fuch , whofe Sides are right ...
... meet , which is called the angular Point . As the Angle DAF fhews the Angle formed by the two Lines or Sides DA , AF ; it being the angular Point wherein the Sides meet . Moreover , right - lined Angles are fuch , whofe Sides are right ...
Page 8
... meet ; as A and B. L H 35. A Paral- lelogram is a qua- drilateral Figure , whose oppofite Sides are parallel or equi- G M diftant ; asGLHM . A E B H 36. In a Pa- rallelogram A B CD , when a Diameter A C , and two Lines F C EF , HI ...
... meet ; as A and B. L H 35. A Paral- lelogram is a qua- drilateral Figure , whose oppofite Sides are parallel or equi- G M diftant ; asGLHM . A E B H 36. In a Pa- rallelogram A B CD , when a Diameter A C , and two Lines F C EF , HI ...
Page 11
... meet on that Side , where the Angles are lefs than two right Angles . 14. Two right Lines do not contain a Space . 15. If to equal things you add unequal things , the excess of the wholes fhall be equal to the excefs of the unequal ...
... meet on that Side , where the Angles are lefs than two right Angles . 14. Two right Lines do not contain a Space . 15. If to equal things you add unequal things , the excess of the wholes fhall be equal to the excefs of the unequal ...
Page 12
... meet with two Numbers in the Margin , the firft fhews the Propofition , the fecond the Book ; as by 4. 1. you are to under- ftand the fourth Propofition of the first Book : and fo of the reft . Moreover , ax . denotes Ax- iom , poft ...
... meet with two Numbers in the Margin , the firft fhews the Propofition , the fecond the Book ; as by 4. 1. you are to under- ftand the fourth Propofition of the first Book : and fo of the reft . Moreover , ax . denotes Ax- iom , poft ...
Page 28
... . duce them till they meet , fuppofe in G : Then the outward Angle AEF will be greater than the inward Angle DFE , to which it was equal by the Hypothefis : Which is abfurd . PROP . PROP . XXVIII . E A- C H F If 28 EUCLID'S Elements .
... . duce them till they meet , fuppofe in G : Then the outward Angle AEF will be greater than the inward Angle DFE , to which it was equal by the Hypothefis : Which is abfurd . PROP . PROP . XXVIII . E A- C H F If 28 EUCLID'S Elements .
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.