Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Page 73
... opposite to the acute Angle BFA : therefore since BA ( BG ) reaches to the Circumference , BF extends farther , and fo the Point F ; and by the same reason , any other Point of the right Line AC , shall be situate with- out the Circle ...
... opposite to the acute Angle BFA : therefore since BA ( BG ) reaches to the Circumference , BF extends farther , and fo the Point F ; and by the same reason , any other Point of the right Line AC , shall be situate with- out the Circle ...
Page 77
... opposite to ngle adjacent to EBC , as is mani- p . 13. 1. and ax . 3 . Circle cannot be described about a because the opposite Angles of it d , or are less than two Right An- D SCHOLIU M. BE In a quadrilateral Figure ( ABCD ) if the ...
... opposite to ngle adjacent to EBC , as is mani- p . 13. 1. and ax . 3 . Circle cannot be described about a because the opposite Angles of it d , or are less than two Right An- D SCHOLIU M. BE In a quadrilateral Figure ( ABCD ) if the ...
Page 96
... angled , on the Side opposite to the right Angle ; and if obtufe - angled , without the Triangle . SCHOL . By the fame way you may describe a. * 31.3 . SCHOL . ner , ter A which 27.3 . COROL . ference 96 EUCLID'S Elements .
... angled , on the Side opposite to the right Angle ; and if obtufe - angled , without the Triangle . SCHOL . By the fame way you may describe a. * 31.3 . SCHOL . ner , ter A which 27.3 . COROL . ference 96 EUCLID'S Elements .
Page 164
... opposite are parallel . XXVII . A Polyhedron is a Solid of many Sides or Faces . A D PROP . I. BT C One part AC of a Right Line cannot be in a Plane , and another part CB with- out the same . F Continue out AC in the Plane to F ; then ...
... opposite are parallel . XXVII . A Polyhedron is a Solid of many Sides or Faces . A D PROP . I. BT C One part AC of a Right Line cannot be in a Plane , and another part CB with- out the same . F Continue out AC in the Plane to F ; then ...
Page 178
... opposite Planes AD , BC ; it shall be as the Base AH is to the Base BH , so is the Solid AHD to the Solid BHC . ne Th I opp Equ T folid : Line a L DF P G M H H N B I A E B K Conceive the Parallelepip . ABCD to be conti- nued out both ...
... opposite Planes AD , BC ; it shall be as the Base AH is to the Base BH , so is the Solid AHD to the Solid BHC . ne Th I opp Equ T folid : Line a L DF P G M H H N B I A E B K Conceive the Parallelepip . ABCD to be conti- nued out both ...
Common terms and phrases
9 ax ABCD abfurd alfo alſo Altitude Angle ABC Bafe Baſe Base BC becauſe biſect Center Circ Circle Circumference Cone conft Conſequent COROL Cylinder demonſtrated deſcribed Diameter draw the right drawn EFGH equal Angles equiangular equilateral Equimultiples faid fame fimilar fince firſt folid fore four right given right Line gles Gnomon greater Hence leſs likewiſe Line CD Magnitudes manifeſt Number oppofite parallel Parallelepip Parallelepipedons Parallelogram perpend perpendicular Point Polyhedron Priſm Probl Proportion Pyramids Q. E. D. PROP Ratio Reaſon Rectangle right Angles right Line AB right Line AC right-lined Figure ſaid ſame ſay SCHOL SCHOLIU ſecond Segment ſhall Side BC ſince ſome Sphere Square ſtand ſuppoſe theſe thoſe tiple Triangle ABC triplicate Whence whole whoſe
Popular passages
Page 29 - 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 143 - 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 31 - 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 25 - 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 29 - 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 217 - ... to one of the consequents, so are all the antecedents to all the consequents ; [V. 12] hence the whole polyhedral solid in the sphere about A as centre has to the whole polyhedral solid in the other sphere the ratio triplicate of that which AB has to the radius of the other sphere, that is, of that which the diameter BD has to the diameter of the other sphere. QED This proposition is of great length and therefore requires summarising in order to make it easier to grasp. Moreover there are some...
Page 9 - 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.
Page 217 - And as one antecedent is to its confequent, fo are all the antecedents to all the confequents. Wherefore the whole folid polyhedron in the greater fphere has to the whole folid polyhedron in the other, the triplicate ratio of that which AB...
Page 217 - Center is A, to every one of the Pyramids of the fame Order in the other Sphere, hath a triplicate Proportion of that which AB has to that Line drawn from the Center of the other Sphere.