Plane and Solid Geometry |
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Page 34
... Rectangle ( C ) , whose angles are all right angles . A B C The Square ( D ) , whose sides are all equal and whose angles are all equal . 105. The square is at once a rhombus and a rectangle . D PROPOSITION XX . THEOREM . 106. In a ...
... Rectangle ( C ) , whose angles are all right angles . A B C The Square ( D ) , whose sides are all equal and whose angles are all equal . 105. The square is at once a rhombus and a rectangle . D PROPOSITION XX . THEOREM . 106. In a ...
Page 36
... rectangle . 4. If two parallels are cut by a third straight line , the bisectors of the four interior angles form a rectangle . ( See 57 , Ex . 3. ) 5. If CE is drawn parallel to BD , meeting AD produced , show that BCED is a parallel ...
... rectangle . 4. If two parallels are cut by a third straight line , the bisectors of the four interior angles form a rectangle . ( See 57 , Ex . 3. ) 5. If CE is drawn parallel to BD , meeting AD produced , show that BCED is a parallel ...
Page 37
... rectangle are equal . 4. Show that two parallelograms are equal when two adjacent sides and the included angle of the one are equal to the two adjacent sides and the included angle of the other . PROPOSITION XXII . THEOREM . 110. If ...
... rectangle are equal . 4. Show that two parallelograms are equal when two adjacent sides and the included angle of the one are equal to the two adjacent sides and the included angle of the other . PROPOSITION XXII . THEOREM . 110. If ...
Page 40
... rectangle . 2. If the non - parallel sides of a trapezoid are equal , the angles which they make with the bases are equal . 3. If from any point in the base of an isosceles triangle parallels to the equal sides are drawn , the perimeter ...
... rectangle . 2. If the non - parallel sides of a trapezoid are equal , the angles which they make with the bases are equal . 3. If from any point in the base of an isosceles triangle parallels to the equal sides are drawn , the perimeter ...
Page 75
... rectangle . PROPOSITION XXVI . PROBLEM . 195. At a given point in a given circumference , to draw a tan- gent to the circumference . Let O be the given circle and 4 the point on its circumference . To draw a tangent through 4 . It is ...
... rectangle . PROPOSITION XXVI . PROBLEM . 195. At a given point in a given circumference , to draw a tan- gent to the circumference . Let O be the given circle and 4 the point on its circumference . To draw a tangent through 4 . It is ...
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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.