Euclid's Elements of Geometry, Libros 1-6Henry Martyn Taylor The University Press, 1893 - 504 páginas |
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Página 7
... point where they meet be equal , each of these angles is called a right angle , and the straight lines are said to ... given straight line CD , the part AE intercepted between the point and the straight line is commonly called the ...
... point where they meet be equal , each of these angles is called a right angle , and the straight lines are said to ... given straight line CD , the part AE intercepted between the point and the straight line is commonly called the ...
Página 9
... a straight line AE be drawn from a point A at right angles to a given straight line CD , the part AE intercepted between the point and the straight line is commonly called the perpendicular from the point A on the straight line CD . Euclid ...
... a straight line AE be drawn from a point A at right angles to a given straight line CD , the part AE intercepted between the point and the straight line is commonly called the perpendicular from the point A on the straight line CD . Euclid ...
Página 17
... 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 ... a given point to draw a PROPOSITION 1 . 17.
... 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 ... a given point to draw a PROPOSITION 1 . 17.
Página 18
Henry Martyn Taylor. PROPOSITION 2 . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it is required to draw from A a straight line equal to BC ...
Henry Martyn Taylor. PROPOSITION 2 . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it is required to draw from A a straight line equal to BC ...
Página 19
... given point is in the given straight line produced . 3. Draw from a given point a straight line ( a ) twice , ( b ) three times the length of a given straight line . 4. Draw from D in any one of the diagrams of Proposition 2 a straight ...
... given point is in the given straight line produced . 3. Draw from a given point a straight line ( a ) twice , ( b ) three times the length of a given straight line . 4. Draw from D in any one of the diagrams of Proposition 2 a straight ...
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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.