Plane and Solid GeometryCharles E. Merrill Company, 1911 - 546 σελίδες |
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Σελίδα 22
... ber of equal parts . Whether it is possible actually thus to divide this angle on paper by use of the ruler and com- passes , is another question . DEMONSTRATION OF GEOMETRIC RELATIONS 52. A geometric proof , or 22 PLANE GEOMETRY.
... ber of equal parts . Whether it is possible actually thus to divide this angle on paper by use of the ruler and com- passes , is another question . DEMONSTRATION OF GEOMETRIC RELATIONS 52. A geometric proof , or 22 PLANE GEOMETRY.
Σελίδα 28
... passing through the point equals two right angles . Thus , 4p + 4q + 2r = 2 rt . 4 . Fig . 2 Fig . 3 EXERCISES . GROUP 3 ... pass through more than three points . BOOK I RECTILINEAR FIGURES PROPOSITION I. THEOREM 78. If one 28 PLANE GEOMETRY.
... passing through the point equals two right angles . Thus , 4p + 4q + 2r = 2 rt . 4 . Fig . 2 Fig . 3 EXERCISES . GROUP 3 ... pass through more than three points . BOOK I RECTILINEAR FIGURES PROPOSITION I. THEOREM 78. If one 28 PLANE GEOMETRY.
Σελίδα 35
... the difference of the other two sides is 12 inches ? Ex . 4. On a given line as base , by exact use of ruler and com- passes , construct an equilateral triangle . PROPOSITION V. THEOREM 95. If , from a point within TRIANGLES 35.
... the difference of the other two sides is 12 inches ? Ex . 4. On a given line as base , by exact use of ruler and com- passes , construct an equilateral triangle . PROPOSITION V. THEOREM 95. If , from a point within TRIANGLES 35.
Σελίδα 46
... kind of a triangle is this ? Ex . 3. By exact use of the ruler and com- passes , draw a perpendicular to a given line from a given point without the line , PROPOSITION XVI . THEOREM 107. If two triangles have two 46 BOOK I. PLANE GEOMETRY.
... kind of a triangle is this ? Ex . 3. By exact use of the ruler and com- passes , draw a perpendicular to a given line from a given point without the line , PROPOSITION XVI . THEOREM 107. If two triangles have two 46 BOOK I. PLANE GEOMETRY.
Σελίδα 64
... passing through the point 2rt . & ) . But / ECD LA , Art . 126 . ( being ext . int . 4 of parallel lines ) . Also LBCE LB , Art . 124 . ( being alt . int . 4 of parallel lines ) . Substituting for ECD its equal , ZA , and for BCE its ...
... passing through the point 2rt . & ) . But / ECD LA , Art . 126 . ( being ext . int . 4 of parallel lines ) . Also LBCE LB , Art . 124 . ( being alt . int . 4 of parallel lines ) . Substituting for ECD its equal , ZA , and for BCE its ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude base bisector bisects chord circumference circumscribed coincide cone of revolution denoted diagonal diameter dihedral angle divided equidistant equilateral triangle equivalent exterior angle figure Find the area Find the radius frustum geometric given circle given line given point Hence homologous sides hypotenuse intersect isosceles trapezoid isosceles triangle lateral area lateral edges Let the pupil line drawn measure midpoints number of sides opposite parallel lines parallelogram parallelopiped pass a plane perimeter perpendicular plane MN plane parallel polyhedron prism prismatoid produced proportional pyramid Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular polygon rhombus right angles right triangle secant segments similar slant height sphere spherical polygon spherical triangle square pyramid surface symmetrical tangent tetrahedron THEOREM trapezoid triangle ABC trihedral vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 241 - If two triangles have an angle of one equal to an angle of the other, and...
Σελίδα 103 - A chord is a straight line joining the extremities of an arc.
Σελίδα 54 - Every point in the bisector of an angle is equidistant from the sides of the angle. Hyp. Z DAB = Z DAC and 0 is any point in AD. To prove 0 is equidistant from AB and AC. Draw OP _L AB and OP' _L AC, and prove the equality of the two triangles.
Σελίδα 82 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Σελίδα 114 - In the same circle or in equal circles, if two chords are unequal, they are unequally distant from the center, and the greater chord is at the less distance.
Σελίδα 47 - If two triangles have two sides of one equal respectively to two sides of the other...
Σελίδα 416 - Every section of a circular cone made by a plane parallel to the base is a circle. Let the section abcd of the circular cone S-ABCD be parallel to the base. To prove that abcd is a circle.
Σελίδα 35 - The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line...
Σελίδα 193 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Σελίδα 450 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. Given the spherical triangle ABC, with angle B equal to angle C. To prove that AC = AB. Proof. Let A A'B'C ' be the polar triangle of A ABC.