The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 45
Euclides. PROP . XLVI . PROB . To describe a square upon a given straight line . Let AB be the given straight line : it is required to describe a square upon AB . From the point A draw AC at right angles to AB ( 1. 11 ) ; make AD equal ...
Euclides. PROP . XLVI . PROB . To describe a square upon a given straight line . Let AB be the given straight line : it is required to describe a square upon AB . From the point A draw AC at right angles to AB ( 1. 11 ) ; make AD equal ...
Página 46
... square described upon the side BC is equal to the squares described upon BA , AC . On BC describe the square BDEC ( 1. 46 ) , and on BA , AC the squares GB , HC ; and through A draw ... AC ; therefore the square upon 46 EUCLID'S ELEMENTS .
... square described upon the side BC is equal to the squares described upon BA , AC . On BC describe the square BDEC ( 1. 46 ) , and on BA , AC the squares GB , HC ; and through A draw ... AC ; therefore the square upon 46 EUCLID'S ELEMENTS .
Página 47
Euclides. HC upon BA , AC ; therefore the square upon the side BC is equal to the squares upon the sides BA , AC . Wherefore , In any right - angled triangle , & c . Q. E. D. PROP . XLVIII . THEOR . If the square described upon one of ...
Euclides. HC upon BA , AC ; therefore the square upon the side BC is equal to the squares upon the sides BA , AC . Wherefore , In any right - angled triangle , & c . Q. E. D. PROP . XLVIII . THEOR . If the square described upon one of ...
Página 49
... AC , and join CE ; bisect CE at F , draw FG perpendicular and equal to CF , and join CG : CFG shall B be the triangle required . A C For the squares on AB , BC , or on BD , BC , are equal to the square ... AC are equal to the squares on CD ...
... AC , and join CE ; bisect CE at F , draw FG perpendicular and equal to CF , and join CG : CFG shall B be the triangle required . A C For the squares on AB , BC , or on BD , BC , are equal to the square ... AC are equal to the squares on CD ...
Página 53
... square of which a given line shall be the diagonal . 10. Take any point D in AB the base of a triangle ABC , right - angled at A ; in DC take DE equal to AC , and bisect CE at F : then shew that DF , BF ( drawn to a point F within the ...
... square of which a given line shall be the diagonal . 10. Take any point D in AB the base of a triangle ABC , right - angled at A ; in DC take DE equal to AC , and bisect CE at F : then shew that DF , BF ( drawn to a point F within the ...
Términos y frases comunes
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore