A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geomentry |
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Page 125
... similitude will evidently be the given ratio M : N. ( 40 ) . 82. Scholium . The point O in the preceding construction is called the centre of similitude of the two polygons . 11 * BOOK IV . COMPARISON AND MEASUREMENT OF THE SURFACES OF ...
... similitude will evidently be the given ratio M : N. ( 40 ) . 82. Scholium . The point O in the preceding construction is called the centre of similitude of the two polygons . 11 * BOOK IV . COMPARISON AND MEASUREMENT OF THE SURFACES OF ...
Page 358
... centre O lies in the radical axis of P and Q ; and for the Fig . 1 . Fig . 2 ... SIMILITUDE OF TWO CIRCLES . 75. Definition . If the straight line joining ... similitude of the two circles . PROPOSITION XXI . - THEOREM . 76. If in two ...
... centre O lies in the radical axis of P and Q ; and for the Fig . 1 . Fig . 2 ... SIMILITUDE OF TWO CIRCLES . 75. Definition . If the straight line joining ... similitude of the two circles . PROPOSITION XXI . - THEOREM . 76. If in two ...
Page 360
... centre of similitude . If they touch internally ( Fig . 2 ) , the point of contact is their external centre of similitude . If one circle is wholly within the other ( Fig . 3 ) , both centres of similitude lie within both circles . Fig ...
... centre of similitude . If they touch internally ( Fig . 2 ) , the point of contact is their external centre of similitude . If one circle is wholly within the other ( Fig . 3 ) , both centres of similitude lie within both circles . Fig ...
Page 361
... centre of similitude of the other two meet in a point ; 2d . The external centres of similitude of the three pairs of circles are in a straight line ; 3d . The external centre of similitude of any pair and the internal centres of ...
... centre of similitude of the other two meet in a point ; 2d . The external centres of similitude of the three pairs of circles are in a straight line ; 3d . The external centre of similitude of any pair and the internal centres of ...
Page 366
... centre of similitude , V , of M and N ( 88 ) . For the same reason , the radical axis of O ' and O " , and the radical axis of O ' and O ' , pass through V. Therefore , V is the radical centre of the three circles 0 , 0 ' , O " . 92 ...
... centre of similitude , V , of M and N ( 88 ) . For the same reason , the radical axis of O ' and O " , and the radical axis of O ' and O ' , pass through V. Therefore , V is the radical centre of the three circles 0 , 0 ' , O " . 92 ...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2015 |
Common terms and phrases
ABCD adjacent angles altitude anharmonic ratio apothem base bisects centre of similitude chord circumference circumscribed coincide common cone Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw edges equally distant equilateral equivalent exterior angle faces figure find the locus frustum given circles given plane given point given straight line hence homologous indefinitely inscribed inscribed angle isosceles Let ABC measure middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Popular passages
Page 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP
Page 129 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 115 - It follows from § 259 that if through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 216 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 74 - An angle formed by a tangent and a chord is measured by onehalf the intercepted arc.
Page 107 - If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon AB...
Page 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 255 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...