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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 78.
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 . G I A H D F 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 . G I A H D F 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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Συχνά εμφανιζόμενοι όροι και φράσεις
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 Let the straight magnitudes meet 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 51 - 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.
Σελίδα 29 - 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 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Σελίδα 11 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Σελίδα 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Σελίδα 84 - 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 80 - 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 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.