Plane and Solid GeometryLongmans, Green and Company, 1898 - 210 σελίδες |
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Σελίδα 16
... 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 are perpendicular to each other . EXERCISES . SUGGESTION . Show ...
... 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 are perpendicular to each other . EXERCISES . SUGGESTION . Show ...
Σελίδα 19
... SUGGESTION . ZAGH = / GHD ; add / GHC . 3. When two straight lines are cut by a third straight line , if the exterior - interior angles be equal , these two straight lines are parallel . E M H B A N D C K SUGGESTION . F If AB is not ...
... SUGGESTION . ZAGH = / GHD ; add / GHC . 3. When two straight lines are cut by a third straight line , if the exterior - interior angles be equal , these two straight lines are parallel . E M H B A N D C K SUGGESTION . F If AB is not ...
Σελίδα 21
... 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 supplementary . KH F ID B E A C L G Let DE be perpendicular to AC ...
... 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 supplementary . KH F ID B E A C L G Let DE be perpendicular to AC ...
Σελίδα 40
... SUGGESTION . See 112 . 115. A Polygon is a plane figure bounded by straight lines ; as ABCDE . The straight lines are called the Sides of the polygon ; and their sum is called the Perimeter of the polygon . The Angles of the polygon are ...
... SUGGESTION . See 112 . 115. A Polygon is a plane figure bounded by straight lines ; as ABCDE . The straight lines are called the Sides of the polygon ; and their sum is called the Perimeter of the polygon . The Angles of the polygon are ...
Σελίδα 53
... to each other , the straight line joining their centres passes through the point of contact . SUGGESTION . Draw a common tangent . PROPOSITION VI . THEOREM . 153. If two circumferences intersect § 152. ] 53 THE CIRCLE .
... to each other , the straight line joining their centres passes through the point of contact . SUGGESTION . Draw a common tangent . PROPOSITION VI . THEOREM . 153. If two circumferences intersect § 152. ] 53 THE CIRCLE .
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 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.
Σελίδα 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Σελίδα 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.