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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 páginas |
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Página 21
... . 1. ) AD equal to AB , and join BD and because ADB is the exterior angle of the triangle BDC , it is greater ( 16. 1. ) than the interior and opposite B D · angle DCB ; but ADB is equal ( 5. OF GEOMETRY . BOOK I. 21.
... . 1. ) AD equal to AB , and join BD and because ADB is the exterior angle of the triangle BDC , it is greater ( 16. 1. ) than the interior and opposite B D · angle DCB ; but ADB is equal ( 5. OF GEOMETRY . BOOK I. 21.
Página 22
... join DC . D A Because DA is equal to AC , the an- gle ADC is likewise equal ( 5. 1. ) to ACD but the angle BCD is greater than the angle ACD ; therefore the an- gle BCD is greater than the angle ADC ; and because the angle BCD of the ...
... join DC . D A Because DA is equal to AC , the an- gle ADC is likewise equal ( 5. 1. ) to ACD but the angle BCD is greater than the angle ACD ; therefore the an- gle BCD is greater than the angle ADC ; and because the angle BCD of the ...
Página 24
... join KF , KG ; the triangle KFG has its sides equal to the three straight lines , A , B , C. Because the point F is the centre of the circle DKL , FD is equal ( 11 . Def . ) to FK ; but FD is equal to the straight line A ; therefore FK ...
... join KF , KG ; the triangle KFG has its sides equal to the three straight lines , A , B , C. Because the point F is the centre of the circle DKL , FD is equal ( 11 . Def . ) to FK ; but FD is equal to the straight line A ; therefore FK ...
Página 25
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG , therefore the base BC is equal ( 4. 1. ) to the base EG ; and be ...
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG , therefore the base BC is equal ( 4. 1. ) to the base EG ; and be ...
Página 26
... join GC ; therefore , because BG is equal to DE , and BC to EF , the two sides GB , BC are equal to the two , DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; therefore the base GC is equal ( 4. 1. ) to the base DF ...
... join GC ; therefore , because BG is equal to DE , and BC to EF , the two sides GB , BC are equal to the two , DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; therefore the base GC is equal ( 4. 1. ) to the base DF ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 41 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 70 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Página 91 - 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. either the sides adjacent to the equal...
Página 273 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...