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 7
... difference , or the part of A remaining , when a part equal to B has been taken away from it . In like manner , A - B + C , or A + C - B , signifies that A and C are to be added together , and that B is to be subtracted from their sum ...
... difference , or the part of A remaining , when a part equal to B has been taken away from it . In like manner , A - B + C , or A + C - B , signifies that A and C are to be added together , and that B is to be subtracted from their sum ...
Página 46
... difference of two given squares . Draw , as in the last problem , ( see the fig . ) the lines AC , AD , at right angles to each other , making AC equal to the side of the less square ; then , from C as centre , with a radius equal to ...
... difference of two given squares . Draw , as in the last problem , ( see the fig . ) the lines AC , AD , at right angles to each other , making AC equal to the side of the less square ; then , from C as centre , with a radius equal to ...
Página 51
... difference , or that AC2 - CD2 = ( AC + CD ) ( AC- . : CD ) . " SCHOLIUM . In this proposition , let AC be denoted ... difference of two quantities , is equivalent to the difference of their squares PROP . VI THEOR . If a straight line ...
... difference , or that AC2 - CD2 = ( AC + CD ) ( AC- . : CD ) . " SCHOLIUM . In this proposition , let AC be denoted ... difference of two quantities , is equivalent to the difference of their squares PROP . VI THEOR . If a straight line ...
Página 53
... difference of the lines . " SCHOLIUM . In this proposition , let AB be denoted by a , and the segments AC and CB by b and c ; then a2 = b2 + 2bc + c2 ; adding c2 to each member of this equality , we shall have , a2 + c2 = b2 + 2bc + 2c2 ...
... difference of the lines . " SCHOLIUM . In this proposition , let AB be denoted by a , and the segments AC and CB by b and c ; then a2 = b2 + 2bc + c2 ; adding c2 to each member of this equality , we shall have , a2 + c2 = b2 + 2bc + 2c2 ...
Página 54
... difference of " the lines AB and BC , four times the rectangle contained by any two " lines , together with the square of their difference , is equal to the square " of the sum of the lines . " " COR . 2. From the demonstration it is ...
... difference of " the lines AB and BC , four times the rectangle contained by any two " lines , together with the square of their difference , is equal to the square " of the sum of the lines . " " COR . 2. From the demonstration it is ...
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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...