Euclid's Elements of Geometry, Libros 1-6;Libro 11Henry Martyn Taylor The University Press, 1895 - 657 páginas |
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Página 76
... parallel . E A B D F C PROOF . AB , CD cannot meet when produced beyond B and D ; for if they did , the exterior ... parallel . Therefore AB , CD are parallel . Wherefore , if a straight line & c . ( Def . 9. ) EXERCISES . 1. No two ...
... parallel . E A B D F C PROOF . AB , CD cannot meet when produced beyond B and D ; for if they did , the exterior ... parallel . Therefore AB , CD are parallel . Wherefore , if a straight line & c . ( Def . 9. ) EXERCISES . 1. No two ...
Página 78
... parallel . Let the straight line EF , intersecting the two straight lines AB , CD , Or ( 1 ) make the exterior angle EGB equal to the interior and opposite angle on the same side GHD , ( 2 ) make the interior angles on the same side BGH ...
... parallel . Let the straight line EF , intersecting the two straight lines AB , CD , Or ( 1 ) make the exterior angle EGB equal to the interior and opposite angle on the same side GHD , ( 2 ) make the interior angles on the same side BGH ...
Página 79
... parallel . 2. If a straight line intersecting two other straight lines make two external angles on opposite sides of the line equal , the two straight lines are parallel . 3. If a straight line intersecting two other straight lines make ...
... parallel . 2. If a straight line intersecting two other straight lines make two external angles on opposite sides of the line equal , the two straight lines are parallel . 3. If a straight line intersecting two other straight lines make ...
Página 80
... parallel straight lines AB , CD : it is required to prove that ( 1 ) the alternate angles AGH , GHD are equal , ( 2 ) ... parallel . ( Post . 9 , page 51. ) But AB , CD are parallel ; therefore the angle AGH is equal to the angle GHD . ( 2 ) ...
... parallel straight lines AB , CD : it is required to prove that ( 1 ) the alternate angles AGH , GHD are equal , ( 2 ) ... parallel . ( Post . 9 , page 51. ) But AB , CD are parallel ; therefore the angle AGH is equal to the angle GHD . ( 2 ) ...
Página 81
... parallel to the base of an isosceles triangle makes equal angles with the sides . 2. If through any point equidistant from two parallel straight lines , two straight lines be drawn cutting the parallel straight lines , they will ...
... parallel to the base of an isosceles triangle makes equal angles with the sides . 2. If through any point equidistant from two parallel straight lines , two straight lines be drawn cutting the parallel straight lines , they will ...
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Términos y frases comunes
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
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Página 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.
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Página 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
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Página 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.