Elements of Plane and Solid GeometryAmerican Book Company, 1903 - 384 σελίδες |
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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 10
... ABC and DEF are equal , whatever may be the length of each side , if angle ABC can be placed B upon angle DEF so that the vertex B shall fall upon vertex E , BC fall upon EF , and BA fall upon ED . [ It should be noticed that angle ABC ...
... ABC and DEF are equal , whatever may be the length of each side , if angle ABC can be placed B upon angle DEF so that the vertex B shall fall upon vertex E , BC fall upon EF , and BA fall upon ED . [ It should be noticed that angle ABC ...
Σελίδα 15
... ABC and DEF have AB = DE , BC = LBLE . = To Prove the ABC and DEF equal in all respects . F EF , and Proof . Place the AABC upon the △ DEF so that B shall coincide with its equal E , BA falling upon ED , and BC upon EF . Since , by ...
... ABC and DEF have AB = DE , BC = LBLE . = To Prove the ABC and DEF equal in all respects . F EF , and Proof . Place the AABC upon the △ DEF so that B shall coincide with its equal E , BA falling upon ED , and BC upon EF . Since , by ...
Σελίδα 17
... ABC and DEF have △ A = ZD , ≤ C = △ F , and AC DF . = To Prove the ABC and DEF equal in all respects . Proof . Place the △ ABC upon the △ DEF , so that A shall coincide with its equal D , AB falling upon DE , and 40 falling upon DF ...
... ABC and DEF have △ A = ZD , ≤ C = △ F , and AC DF . = To Prove the ABC and DEF equal in all respects . Proof . Place the △ ABC upon the △ DEF , so that A shall coincide with its equal D , AB falling upon DE , and 40 falling upon DF ...
Σελίδα 20
... DEF be 2 R.A.'s . To Prove ABC = DEF . F Proof . Suppose them to be unequal and that ABC , when superimposed upon DEF , takes the position GEF . Then at E there would be two perpendiculars to EF , which contradicts § 40 . Therefore the ...
... DEF be 2 R.A.'s . To Prove ABC = DEF . F Proof . Suppose them to be unequal and that ABC , when superimposed upon DEF , takes the position GEF . Then at E there would be two perpendiculars to EF , which contradicts § 40 . Therefore the ...
Σελίδα 28
Alan Sanders. 72. DEFINITION . One proposition is the converse of another , when the hypothesis and conclusion of one are respectively the conclusion and hypothesis of the other . The ... ABC and DEF are R.A. A equal 28 PLANE GEOMETRY.
Alan Sanders. 72. DEFINITION . One proposition is the converse of another , when the hypothesis and conclusion of one are respectively the conclusion and hypothesis of the other . The ... ABC and DEF are R.A. A equal 28 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.