Euclid's Elements of Geometry, Libros 1-6Henry Martyn Taylor The University Press, 1893 - 504 páginas |
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Página 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 ...
Página 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 ...
Página 10
... diagonal * . The surface contained within a closed figure is called the area of the figure . A closed rectilineal ... diagonals . E It will be observed that a closed figure has the same number of angles as it has sides . If a closed ...
... diagonal * . The surface contained within a closed figure is called the area of the figure . A closed rectilineal ... diagonals . E It will be observed that a closed figure has the same number of angles as it has sides . If a closed ...
Página 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 ...
Página 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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Términos y frases comunes
ABCD AC is equal ADDITIONAL PROPOSITION angle ACB angle BAC angles ABC anharmonic arc ABC bisected centre of similitude chord circle ABC coincide Constr Coroll cut the circle describe a circle diagonal diameter draw equal angles equal circles equal to CD equiangular equimultiples Euclid EXERCISES exterior angle given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed intersect Let ABC meet middle points opposite sides pair parallel parallelogram pencil pentagon perpendicular polygon PROOF Prop PROPOSITION 14 Ptolemy's Theorem quadrilateral radical axis radius rectangle contained required to prove respectively rhombus right angles shew sides BC Similarly square on AC straight line &c straight line drawn straight line joining subtend tangent theorem triangle ABC triangle DEF triangles are equal twice the rectangle vertices Wherefore
Pasajes populares
Página 59 - Any two sides of a triangle are together greater than the third side.
Página 7 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.
Página 68 - 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.
Página 144 - 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...
Página 376 - 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.
Página 135 - 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.
Página 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 305 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Página 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Página 248 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.