Plane and Solid Geometry |
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Page vi
... show that the solution was correct . This does not appear to me to be in the line of discovery . I have in all cases started with a statement of those known facts which plainly suggest the first step in the solution , then introduced ...
... show that the solution was correct . This does not appear to me to be in the line of discovery . I have in all cases started with a statement of those known facts which plainly suggest the first step in the solution , then introduced ...
Page 11
... show that angle COA is equal to angle AOD . 6. If the angles BOA , EOC , and COB are in the ratio of 2 : 3 : 5 , how many degrees are there in each ? 7. If the angles BOA , BOC , AOD , and COD are in the ratio of 1 : 2 : 34 , how many ...
... show that angle COA is equal to angle AOD . 6. If the angles BOA , EOC , and COB are in the ratio of 2 : 3 : 5 , how many degrees are there in each ? 7. If the angles BOA , BOC , AOD , and COD are in the ratio of 1 : 2 : 34 , how many ...
Page 16
... show that the theorem is true . 2. Prove that the bisectors of two vertical angles are in the same straight line . SUGGESTION . Show that the sum of the angles on one side of FE are equal to the sum of those on the other side . 3. Prove ...
... show that the theorem is true . 2. Prove that the bisectors of two vertical angles are in the same straight line . SUGGESTION . Show that the sum of the angles on one side of FE are equal to the sum of those on the other side . 3. Prove ...
Page 21
... show that the straight lines CB and AD are parallel . SUGGESTION . Apply CEB to DEA , and show that A = LB. E A B PROPOSITION XI . THEOREM . 64. Two angles having their sides perpendicular each to each , are either equal or ...
... show that the straight lines CB and AD are parallel . SUGGESTION . Apply CEB to DEA , and show that A = LB. E A B PROPOSITION XI . THEOREM . 64. Two angles having their sides perpendicular each to each , are either equal or ...
Page 26
... Show that the sum of the distances of any point in a triangle from the three angles is greater than half the sum of the three sides of the triangle . DB + DA + DC > { ( AB + BC + AC ) . PROPOSITION XIII . B THEOREM . A C 86. Two ...
... Show that the sum of the distances of any point in a triangle from the three angles is greater than half the sum of the three sides of the triangle . DB + DA + DC > { ( AB + BC + AC ) . PROPOSITION XIII . B THEOREM . A C 86. Two ...
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Common terms and phrases
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Popular passages
Page 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 108 - Two triangles having 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 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Page 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.