Plane and Solid Geometry |
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Page 13
... any point on this perpendicular , it is true that every point on the perpendicular bisector of a straight line is equally distant from the extremities of that line . 55. COR . 2. When CAD was revolved , it $ 54. ] 13 RECTILINEAR FIGURES .
... any point on this perpendicular , it is true that every point on the perpendicular bisector of a straight line is equally distant from the extremities of that line . 55. COR . 2. When CAD was revolved , it $ 54. ] 13 RECTILINEAR FIGURES .
Page 14
... bisector of the latter . PROPOSITION VI . THEOREM . 57. If two lines are drawn from a point to the extremities of a straight line , their sum is greater than the sum of two other lines similarly drawn , but enveloped by them . D E B Let ...
... bisector of the latter . PROPOSITION VI . THEOREM . 57. If two lines are drawn from a point to the extremities of a straight line , their sum is greater than the sum of two other lines similarly drawn , but enveloped by them . D E B Let ...
Page 16
... 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 that the bisectors of two supplementary angles ...
... 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 that the bisectors of two supplementary angles ...
Page 31
... bisectors of the equal B angles of an isosceles triangle form with the base another isosceles triangle ; that is , DBC is isosceles . 6. What are the relative values of the verti- cal angles D and A in the above ? 7. Show that a ...
... bisectors of the equal B angles of an isosceles triangle form with the base another isosceles triangle ; that is , DBC is isosceles . 6. What are the relative values of the verti- cal angles D and A in the above ? 7. Show that a ...
Page 32
... bisector of B. .. the three lines meeting in O are bisectors of the angles . 97. COR . Since OP = OK = OH , it is shown that the bisec- tors of angles are equally distant from their sides . EXERCISES , 1. Show that the three ...
... bisector of B. .. the three lines meeting in O are bisectors of the angles . 97. COR . Since OP = OK = OH , it is shown that the bisec- tors of angles are equally distant from their sides . EXERCISES , 1. Show that the three ...
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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.