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 Sperical TrigonometryW.E. Dean, 1844 - 317 Seiten |
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Seite 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 ...
Seite 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 ...
Seite 51
... difference , or that AC2 - CD2 = ( AC + ČD ) ( AC— CD ) . " 66 SCHOLIUM . In this proposition , let AC be denoted by ... 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 + ČD ) ( AC— CD ) . " 66 SCHOLIUM . In this proposition , let AC be denoted by ... difference of two quantities , is equivalent to the difference of their squares PROP . VI THEOR . If a straight line ...
Seite 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 a2-62 + 2bc + c2 ; adding c2 to each member of this equality , we shall have , a2 + c2b2 + 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 a2-62 + 2bc + c2 ; adding c2 to each member of this equality , we shall have , a2 + c2b2 + 2bc + 2c2 ...
Seite 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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Häufige Begriffe und Wortgruppen
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder 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 magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
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Seite 95 - 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...
Seite 68 - THE angles in the same segment of a circle are equal to one another...
Seite 23 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Seite 74 - 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.
Seite 78 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Seite 9 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Seite 75 - If a straight line touch a circle, and from the point of contact a...
Seite 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Seite 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.