Plane and Solid GeometryCharles E. Merrill Company, 1911 - 546 σελίδες |
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Σελίδα 11
... properties in common may be grouped together , and dealt with in the groups formed . 5. Geometry as a science . Definition . The above illus- trations serve to show how advantageous it often is to deal with geometric magnitudes by ...
... properties in common may be grouped together , and dealt with in the groups formed . 5. Geometry as a science . Definition . The above illus- trations serve to show how advantageous it often is to deal with geometric magnitudes by ...
Σελίδα 12
Fletcher Durell. separately ; but , by determining the properties of a geometric solid , we determine once for all the properties of every physical solid , no matter what its material , that will exactly fill the space occupied by the ...
Fletcher Durell. separately ; but , by determining the properties of a geometric solid , we determine once for all the properties of every physical solid , no matter what its material , that will exactly fill the space occupied by the ...
Σελίδα 21
... properties in all its parts . It has already been assumed in some of the definitions given . See Arts . 15 and 35 . 3. Through a given point one straight line and only one can be drawn parallel to another given straight line . By Art ...
... properties in all its parts . It has already been assumed in some of the definitions given . See Arts . 15 and 35 . 3. Through a given point one straight line and only one can be drawn parallel to another given straight line . By Art ...
Σελίδα 23
... A scholium is a remark made upon some particular feature of a proposition , or upon two or more propositions which are compared . 59. Hypothesis and conclusion . A proposition consists of two DEMONSTRATION OF PROPERTIES 23.
... A scholium is a remark made upon some particular feature of a proposition , or upon two or more propositions which are compared . 59. Hypothesis and conclusion . A proposition consists of two DEMONSTRATION OF PROPERTIES 23.
Σελίδα 25
... letters Q. E. D. , standing for " quod erat demon- strandum , " and meaning " which was to be proved , " are usually annexed at the end of a completed demonstration . ure EXERCISES . GROUP 2 Ex . 1. In the DEMONSTRATION OF PROPERTIES 25.
... letters Q. E. D. , standing for " quod erat demon- strandum , " and meaning " which was to be proved , " are usually annexed at the end of a completed demonstration . ure EXERCISES . GROUP 2 Ex . 1. In the DEMONSTRATION OF PROPERTIES 25.
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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.