Elements of Plane and Solid GeometryAmerican Book Company, 1903 - 384 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 13
... drawn joining two points . [ It follows from this axiom that two straight lines can intersect in only one point . ] 14. The shortest distance from one point to another is meas- ured on the straight line joining them . 15. Through a ...
... drawn joining two points . [ It follows from this axiom that two straight lines can intersect in only one point . ] 14. The shortest distance from one point to another is meas- ured on the straight line joining them . 15. Through a ...
Σελίδα 21
Alan Sanders. PROPOSITION IV . THEOREM 47. If a perpendicular is drawn to a line at its middle point , I. Any point ... Draw PA and PB . [ It is required to prove PA = PB , for PA and PB measure the distance from P to A and B respectively ...
Alan Sanders. PROPOSITION IV . THEOREM 47. If a perpendicular is drawn to a line at its middle point , I. Any point ... Draw PA and PB . [ It is required to prove PA = PB , for PA and PB measure the distance from P to A and B respectively ...
Σελίδα 23
... drawn to CD at its middle point . By § 48 both m and n must be on this perpendicular . By hypothesis both m and n are on AB . m n So the perpendicular and AB both pass through m and n . By Axiom 13 only one straight line can pass ...
... drawn to CD at its middle point . By § 48 both m and n must be on this perpendicular . By hypothesis both m and n are on AB . m n So the perpendicular and AB both pass through m and n . By Axiom 13 only one straight line can pass ...
Σελίδα 30
... Draw BD bisecting AC . ( § 55. ) B and D are each equally distant from a 21 and 22 are R.A.'s . ( ? ) and C ; Α Show ... drawn making 21 = 22 . Prove 23 = 24 . A C 3 4 A E PROPOSITION XI . THEOREM 85. If two triangles have three 30 PLANE ...
... Draw BD bisecting AC . ( § 55. ) B and D are each equally distant from a 21 and 22 are R.A.'s . ( ? ) and C ; Α Show ... drawn making 21 = 22 . Prove 23 = 24 . A C 3 4 A E PROPOSITION XI . THEOREM 85. If two triangles have three 30 PLANE ...
Σελίδα 32
... Draw a perpendicular to AB from the point C. 91. EXERCISE . If the line AB ( see § 89 ) were situated at the bottom of this page , and there were no room below it for the point E , how could the perpen- dicular be drawn ? THEOREM ...
... Draw a perpendicular to AB from the point C. 91. EXERCISE . If the line AB ( see § 89 ) were situated at the bottom of this page , and there were no room below it for the point E , how could the perpen- dicular be drawn ? THEOREM ...
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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.