Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page 163
... Sphere is the Same with that of the Semicircle . XVII . The Diameter of a Sphere , is a Right Line drawn thro the Center , and terminated on ei- ther Side by the Superficies of the Sphere . XVIII . A Cone is a Figure described when one ...
... Sphere is the Same with that of the Semicircle . XVII . The Diameter of a Sphere , is a Right Line drawn thro the Center , and terminated on ei- ther Side by the Superficies of the Sphere . XVIII . A Cone is a Figure described when one ...
Page 213
... Sphere FGH . e 1 Cut the Spheres by a Plane passing thro ' the Centre A , and the Sections will be concentrick Circles BCDE , FGH . For since a Sphere is made by turning a Semicircle about the Dia- def . 14 . meter at refst ; in ...
... Sphere FGH . e 1 Cut the Spheres by a Plane passing thro ' the Centre A , and the Sections will be concentrick Circles BCDE , FGH . For since a Sphere is made by turning a Semicircle about the Dia- def . 14 . meter at refst ; in ...
Page 214
... Sphere , which will be per- pendicular to the Plane of the Circle BCDE . Again , the Quadrants BE , BX , KX of the equal Semicircles BED , BXD , KXD , are equal ; and so if the Sides of a Polygon BO , OP , PR , RX , KS , ST , TY , YX ...
... Sphere , which will be per- pendicular to the Plane of the Circle BCDE . Again , the Quadrants BE , BX , KX of the equal Semicircles BED , BXD , KXD , are equal ; and so if the Sides of a Polygon BO , OP , PR , RX , KS , ST , TY , YX ...
Page 215
... Sphere , composed of Pyramids , and Triangles , which does not touch the Superficies of the lesser Sphere . 2 2 2 2 def . 3.11 . From the Centre A drawh AZ perpend . to 1 . the Plane KBOS , and join BZ , ZK . Now fince AZ is perpend ...
... Sphere , composed of Pyramids , and Triangles , which does not touch the Superficies of the lesser Sphere . 2 2 2 2 def . 3.11 . From the Centre A drawh AZ perpend . to 1 . the Plane KBOS , and join BZ , ZK . Now fince AZ is perpend ...
Page 216
... Sphere BCDE , to the folid Polyhedron described in that other Sphere , shall have a triplicate Proportion of that which the Diameter of the Sphere BCDE hath to the Diameter of that other Sphere . For the Solids being divided into ...
... Sphere BCDE , to the folid Polyhedron described in that other Sphere , shall have a triplicate Proportion of that which the Diameter of the Sphere BCDE hath to the Diameter of that other Sphere . For the Solids being divided into ...
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.