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 76.
Σελίδα 14
... third case , a straight line can be drawn to intersect the figure in four points . POSTULATE 8. Any line joining two points one within and the other without a closed figure must intersect the figure in one point at least . It follows ...
... third case , a straight line can be drawn to intersect the figure in four points . POSTULATE 8. Any line joining two points one within and the other without a closed figure must intersect the figure in one point at least . It follows ...
Σελίδα 15
... third case one of the paths from A to B represented by part of the dotted line intersects the figure in one point ... third , the first is greater than the third . Such propositions as the above we shall use freely in the following pages ...
... third case one of the paths from A to B represented by part of the dotted line intersects the figure in one point ... third , the first is greater than the third . Such propositions as the above we shall use freely in the following pages ...
Σελίδα 17
... third angular point of an equilateral triangle on the given straight line ; there are thus two triangles which can be constructed satisfying the requirements of the proposition . We say therefore that the problem put before us in this ...
... third angular point of an equilateral triangle on the given straight line ; there are thus two triangles which can be constructed satisfying the requirements of the proposition . We say therefore that the problem put before us in this ...
Σελίδα 23
... third side makes with the equal sides be equal , the other angles are equal . 4. Prove by the method of superposition that , if in two quadri- laterals ABCD , A'B'C'D ' , the sides AB , BC , CD be equal to the sides A'B ' , B'C ' , C'D ...
... third side makes with the equal sides be equal , the other angles are equal . 4. Prove by the method of superposition that , if in two quadri- laterals ABCD , A'B'C'D ' , the sides AB , BC , CD be equal to the sides A'B ' , B'C ' , C'D ...
Σελίδα 24
... third side are equal . Let ABC be a triangle , in which AB is equal to AC , and AB , AC are produced to D , E : it is required to prove that the angle ACB is equal to the angle ABC , and the angle BCE to the angle CBD . CONSTRUCTION ...
... third side are equal . Let ABC be a triangle , in which AB is equal to AC , and AB , AC are produced to D , E : it is required to prove that the angle ACB is equal to the angle ABC , and the angle BCE to the angle CBD . CONSTRUCTION ...
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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.