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 σελίδες |
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Σελίδα 23
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . PROP . XXII . PROB ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . PROP . XXII . PROB ...
Σελίδα 34
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is com- mon ; therefore the whole , or the remainder , AE is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; now AB is also equal to DC ; therefore ...
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is com- mon ; therefore the whole , or the remainder , AE is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; now AB is also equal to DC ; therefore ...
Σελίδα 37
... parallelogram , and AK its diameter , the triangle AEK is equal to the triangle AHK : For the same reason , the triangle KGC is equal to the A H D E K F B G C triangle KFC . Then , because the triangle AEK is OF GEOMETRY . BOOK I. 37.
... parallelogram , and AK its diameter , the triangle AEK is equal to the triangle AHK : For the same reason , the triangle KGC is equal to the A H D E K F B G C triangle KFC . Then , because the triangle AEK is OF GEOMETRY . BOOK I. 37.
Σελίδα 40
... reason , AB and AH are in the same straight line . Now be- cause the angle DBC is equal to the angle FBA , each of them being a right angle , adding to each the angle ABC , the whole angle DBA will be equal ( 2. Ax . ) to the whole FBC ...
... reason , AB and AH are in the same straight line . Now be- cause the angle DBC is equal to the angle FBA , each of them being a right angle , adding to each the angle ABC , the whole angle DBA will be equal ( 2. Ax . ) to the whole FBC ...
Σελίδα 43
... reason , GAC is equal to GDE ; there consequently remains the an- gle BAC EDF . I A D COR . If BA , AC be produced to I and H , the angle BAC HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . The restriction of this ...
... reason , GAC is equal to GDE ; there consequently remains the an- gle BAC EDF . I A D COR . If BA , AC be produced to I and H , the angle BAC HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . The restriction of this ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 68 - THE angles in the same segment of a circle are equal to one another...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 75 - If a straight line touch a circle, and from the point of contact a...
Σελίδα 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...
Σελίδα 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.