Euclid's Elements of Geometry, Bøker 1-6;Bok 11Henry Martyn Taylor The University Press, 1895 - 657 sider |
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Side vi
... diagonal , which do not occur in Euclid's list . The chief alteration in the definitions is in that of the word figure , which is in the Greek text defined to be " that which is enclosed by one or more boundaries . " I have preferred to ...
... diagonal , which do not occur in Euclid's list . The chief alteration in the definitions is in that of the word figure , which is in the Greek text defined to be " that which is enclosed by one or more boundaries . " I have preferred to ...
Side xi
... diagonal of the square in his constructions in Propositions 4 to 8 can scarcely be considered elegant . It is curious to notice that Euclid after giving a demonstration of Proposition 1 makes no use whatever of the theorem . It seems ...
... diagonal of the square in his constructions in Propositions 4 to 8 can scarcely be considered elegant . It is curious to notice that Euclid after giving a demonstration of Proposition 1 makes no use whatever of the theorem . It seems ...
Side 10
... diagonal * . The surface contained within a closed figure is called the area of the figure . A closed rectilineal figure ... diagonals . B D E It will be observed that a closed figure has the same number of angles as it has sides . If a ...
... diagonal * . The surface contained within a closed figure is called the area of the figure . A closed rectilineal figure ... diagonals . B D E It will be observed that a closed figure has the same number of angles as it has sides . If a ...
Side 23
... diagonals AC , BD are equal . 3. If in a quadrilateral two opposite sides be equal , and the angles which a third side makes with the equal sides be equal , the other angles are equal . 4. Prove by the method of superposition that , if ...
... diagonals AC , BD are equal . 3. If in a quadrilateral two opposite sides be equal , and the angles which a third side makes with the equal sides be equal , the other angles are equal . 4. Prove by the method of superposition that , if ...
Side 25
... diagonal AC bisects each of the angles BAD , BCD . 4. If in a quadrilateral ABCD , AB be equal to AD and BC to DC , the diagonal BD is bisected at right angles by the diagonal AC . 5. Prove that the triangle , whose vertices are the ...
... diagonal AC bisects each of the angles BAD , BCD . 4. If in a quadrilateral ABCD , AB be equal to AD and BC to DC , the diagonal BD is bisected at right angles by the diagonal AC . 5. Prove that the triangle , whose vertices are the ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 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...
Side 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Side 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.