Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 45
Page 65
... passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in the same straight line , one circumference may be made to pass , and ...
... passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in the same straight line , one circumference may be made to pass , and ...
Page 66
... pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two circumferences passing through the ...
... pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two circumferences passing through the ...
Page 72
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
Page 77
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : then will it be measured by half of the arc DE . For , draw the radius CD . The external angle BOOK III . 77.
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : then will it be measured by half of the arc DE . For , draw the radius CD . The external angle BOOK III . 77.
Page 89
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
Other editions - View all
Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence