Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 9
... angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or ... ACB . to DFE . B A E D F For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D ...
... angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or ... ACB . to DFE . B A E D F For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D ...
Página 10
... angle BAC = DEF . PROP . III . THEOR . The angles at the base of an isosceles triangle are equal to one another ... ACB ; the side AB is also equal to the side AC . For , if AB be not equal to AC , 10 ELEMENTS.
... angle BAC = DEF . PROP . III . THEOR . The angles at the base of an isosceles triangle are equal to one another ... ACB ; the side AB is also equal to the side AC . For , if AB be not equal to AC , 10 ELEMENTS.
Página 11
... ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the ...
... ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the ...
Página 12
... angle BGA , and the angle CAG equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is ... ACB equal to the angle GCB . PROP . VI . 5 THEOR . The angles which one straight line makes with another upon one ...
... angle BGA , and the angle CAG equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is ... ACB equal to the angle GCB . PROP . VI . 5 THEOR . The angles which one straight line makes with another upon one ...
Página 14
... angles together are less than two right angles . A Produce BC to D ; and because ACD is the exterior angle of the trian- gle ABC , ACD is greater ( 9. 1. ) than the interior and opposite angle ABC ; to each of these add the angle ACB ...
... angles together are less than two right angles . A Produce BC to D ; and because ACD is the exterior angle of the trian- gle ABC , ACD is greater ( 9. 1. ) than the interior and opposite angle ABC ; to each of these add the angle ACB ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore