Euclid's Elements of Geometry, Βιβλία 1-6;Βιβλίο 11Henry Martyn Taylor The University Press, 1895 - 657 σελίδες |
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Αποτελέσματα 1 - 5 από τα 66.
Σελίδα 27
... base of an isosceles triangle be bisected by the straight lines BD and CD , DBC will be an isosceles triangle . 2. BAC is a triangle having the angle B double of the angle A. If BD bisect the angle B and meet AC at D , BD is equal to AD ...
... base of an isosceles triangle be bisected by the straight lines BD and CD , DBC will be an isosceles triangle . 2. BAC is a triangle having the angle B double of the angle A. If BD bisect the angle B and meet AC at D , BD is equal to AD ...
Σελίδα 39
... base BC of a triangle ABC any point D is taken . Draw a straight line such that , if the triangle ABC be folded along this straight line , the point A shall fall upon the point D. PROPOSITION 12 . To draw a straight line at right ...
... base BC of a triangle ABC any point D is taken . Draw a straight line such that , if the triangle ABC be folded along this straight line , the point A shall fall upon the point D. PROPOSITION 12 . To draw a straight line at right ...
Σελίδα 47
... base : prove that the straight lines thus intercepted between the vertex of the isosceles triangle , and this straight line , are together equal to the two equal sides of the triangle . PROPOSITION 16 . An exterior angle of a triangle ...
... base : prove that the straight lines thus intercepted between the vertex of the isosceles triangle , and this straight line , are together equal to the two equal sides of the triangle . PROPOSITION 16 . An exterior angle of a triangle ...
Σελίδα 53
... base BC between B and C of an isosceles triangle ABC , AD is less than AB . 3. Prove that , if AB , AC , AD be equal straight lines , and AC fall within the angle BAD , BD is greater than either BC or CD . 4. ABCD is a quadrilateral of ...
... base BC between B and C of an isosceles triangle ABC , AD is less than AB . 3. Prove that , if AB , AC , AD be equal straight lines , and AC fall within the angle BAD , BD is greater than either BC or CD . 4. ABCD is a quadrilateral of ...
Σελίδα 55
... base of a triangle is divided into two parts by the perpen- dicular from the opposite vertex : prove that each part of the base is less than the adjacent side of the triangle . 3. A straight line drawn from the vertex of an isosceles ...
... base of a triangle is divided into two parts by the perpen- dicular from the opposite vertex : prove that each part of the base is less than the adjacent side of the triangle . 3. A straight line drawn from the vertex of an isosceles ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD ADDITIONAL PROPOSITION AE is equal angle ABC angle ACB angle BAC angular points bisected bisectors centre of similitude chord circle ABC circumscribed circle coincide CONSTRUCTION Coroll cut the circle describe a circle diagonals diameter equal angles equiangular equilateral triangle Euclid EXERCISES figure fixed point given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed circle intersect isosceles triangle Let ABC locus magnitudes meet middle points opposite sides pairs parallel parallelepiped parallelogram perpendicular plane angles polygon PROOF Prop quadrilateral radical axis radius rectangle contained regular polygon required to prove respectively rhombus right angles right-angled triangle shew side BC Similarly solid angle sphere square on AC straight line drawn straight line joining tangent tetrahedron theorem triangle ABC triangles are equal trihedral angle twice the rectangle vertex vertices Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 70 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 218 - The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.
Σελίδα 279 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Σελίδα 148 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.
Σελίδα 137 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 372 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Σελίδα 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Σελίδα 303 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Σελίδα 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Σελίδα 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.