Plane and Solid GeometryCentury Company, 1906 - 418 σελίδες |
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Αποτελέσματα 1 - 5 από τα 45.
Σελίδα 36
... Homologous lines or angles in mutually equiangular polygons are lines or angles similarly situated . 166 COROLLARY 2. In equal triangles , the homologous sides are equal and the homologous angles are equal . PROPOSITION XV . THEOREM 167 ...
... Homologous lines or angles in mutually equiangular polygons are lines or angles similarly situated . 166 COROLLARY 2. In equal triangles , the homologous sides are equal and the homologous angles are equal . PROPOSITION XV . THEOREM 167 ...
Σελίδα 37
... are equal if a leg and an acute angle of the one are equal respectively to a leg and the homologous acute angle of the other . * This proposition is attributed to Thales . PROPOSITION XVI . THEOREM 170 If two sides of one TRIANGLES 37.
... are equal if a leg and an acute angle of the one are equal respectively to a leg and the homologous acute angle of the other . * This proposition is attributed to Thales . PROPOSITION XVI . THEOREM 170 If two sides of one TRIANGLES 37.
Σελίδα 38
... homologous sides of equal A. " § 166 Now DC + DB " > B " C . " Any side of a △ < the sum of the other two sides . " § 160 .. DC + DB > B'C . Or BC > B " C or B'C ' . Q. E. D. PROPOSITION XVII . THEOREM 171 If two sides of one 38 PLANE ...
... homologous sides of equal A. " § 166 Now DC + DB " > B " C . " Any side of a △ < the sum of the other two sides . " § 160 .. DC + DB > B'C . Or BC > B " C or B'C ' . Q. E. D. PROPOSITION XVII . THEOREM 171 If two sides of one 38 PLANE ...
Σελίδα 41
... homologous of equal A. ” § 172 Q. E. D. 174 COROLLARY 1. The straight line drawn from the vertex of an isosceles triangle to the middle point of the base bisects the vertical angle and is perpendicular to the base . 175 COROLLARY 2. An ...
... homologous of equal A. ” § 172 Q. E. D. 174 COROLLARY 1. The straight line drawn from the vertex of an isosceles triangle to the middle point of the base bisects the vertical angle and is perpendicular to the base . 175 COROLLARY 2. An ...
Σελίδα 42
... homologous acute of the other . ' ... AB = AC , § 169 " being homologous sides of equal △ . " § 166 Q. E. D. 177 COROLLARY . An equiangular triangle is equilateral . EXERCISES 59 HK is drawn parallel to BC the base of the isosceles ...
... homologous acute of the other . ' ... AB = AC , § 169 " being homologous sides of equal △ . " § 166 Q. E. D. 177 COROLLARY . An equiangular triangle is equilateral . EXERCISES 59 HK is drawn parallel to BC the base of the isosceles ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal arc BC assigned quantity base bisectors bisects chord circumference circumscribed Compute CONCLUSION cone construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equiangular polygon equidistant equilateral triangle exterior angle Find the area Find the locus frustum given circle given line given point homologous hypotenuse HYPOTHESIS inches inscribed intersect isosceles trapezoid isosceles triangle lateral area legs lune median mid-points number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron prism PROOF Draw PROOF Let Prove pyramid Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular polygon rhombus right angles right triangle SCHOLIUM secant segment semicircle spherical angle spherical degrees spherical excess spherical polygon spherical triangle straight line surface symmetrical tangent tetraedron THEOREM trapezoid triangle ABC triedral vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 168 - 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 41 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 35 - Any side of a triangle is less than the sum of the other two sides...
Σελίδα 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Σελίδα 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Σελίδα 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 199 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Σελίδα 192 - The areas of two rectangles having equal altitudes are to each other as their bases.
Σελίδα 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...