Elements of Plane and Solid GeometryAmerican Book Company, 1903 - 384 σελίδες |
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Αποτελέσματα 6 - 10 από τα 52.
Σελίδα 32
... greater than one half of CD , describe an arc ; with D as a center , and with the same radius , describe an arc intersecting the first are at E. Draw PE . Show that PE is perpendicular to CD . Q.E.F. A. 90. EXERCISE . Draw a ...
... greater than one half of CD , describe an arc ; with D as a center , and with the same radius , describe an arc intersecting the first are at E. Draw PE . Show that PE is perpendicular to CD . Q.E.F. A. 90. EXERCISE . Draw a ...
Σελίδα 34
... greater than one half of DE , describe an arc ; with E as a center , and with the same radius , describe an arc intersecting this arc at F. Join B and F. Then will BF bisect ABC . Draw FE and FD . Prove BEF and BDF equal in all respects ...
... greater than one half of DE , describe an arc ; with E as a center , and with the same radius , describe an arc intersecting this arc at F. Join B and F. Then will BF bisect ABC . Draw FE and FD . Prove BEF and BDF equal in all respects ...
Σελίδα 50
... greater than the third side , but the difference of two sides of a triangle is less than the third side . B E A Let To Prove Proof . Apply axiom 14 . Let To Prove Proof . F ABC be any Δ . AB + BC > AC . Q.E.D. DEF be any A. DE - EF < DF ...
... greater than the third side , but the difference of two sides of a triangle is less than the third side . B E A Let To Prove Proof . Apply axiom 14 . Let To Prove Proof . F ABC be any Δ . AB + BC > AC . Q.E.D. DEF be any A. DE - EF < DF ...
Σελίδα 51
... greater than the semi - perimeter . Prove OA + OB + OC > 1 ( AB + BC + CA ) . A B C 173. DEFINITION . A medial line of a triangle ( or simply a median ) is a line drawn from any vertex of the triangle to the middle point of the opposite ...
... greater than the semi - perimeter . Prove OA + OB + OC > 1 ( AB + BC + CA ) . A B C 173. DEFINITION . A medial line of a triangle ( or simply a median ) is a line drawn from any vertex of the triangle to the middle point of the opposite ...
Σελίδα 52
... less than the perimeter of the triangle . 180. EXERCISE . Prove that the perimeter of the star is greater than that of the polygon ABCDEF . A E PROPOSITION XXVIII . THEOREM 181. If two triangles have two 52 PLANE GEOMETRY.
... less than the perimeter of the triangle . 180. EXERCISE . Prove that the perimeter of the star is greater than that of the polygon ABCDEF . A E PROPOSITION XXVIII . THEOREM 181. If two triangles have two 52 PLANE GEOMETRY.
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC AB² ABC and DEF AC² altitude angle formed angles are equal angles equal apothem bisector bisects chord circum circumference cone Construct a triangle COROLLARY cylinder DEFINITION diagonals diameter dihedral angles divided Draw EFGH equally distant equiangular polygon equilateral triangle equivalent EXERCISE exterior angles Find frustum given circle given line given point hypotenuse inscribed angle isosceles triangle joining the middle lateral area Let ABC Let To Prove line joining medians meet middle points number of sides opposite sides parallel parallelogram parallelopiped perimeter perpendicular point of intersection polyhedron prism prolonged PROPOSITION Prove ABCD pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons slant height sphere spherical square straight line surface tangent tetrahedron THEOREM trapezoid triangle ABC trihedral unequal vertex vertical angle volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 167 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 139 - A line parallel to one side of a triangle divides the other two sides proportionally.
Σελίδα 187 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 202 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 180 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Σελίδα 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Σελίδα 195 - Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig.
Σελίδα 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Σελίδα 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Σελίδα 17 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.