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
... 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 . 22. Multiplication is expressed by an oblique cross , by a point , or by simple apposition : thus ...
... 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 . 22. Multiplication is expressed by an oblique cross , by a point , or by simple apposition : thus ...
Página 20
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . PROP . XV . THEOR . If two straight lines cut one another , the vertical , or ...
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . PROP . XV . THEOR . If two straight lines cut one another , the vertical , or ...
Página 21
... manner , if the side BC be bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . A E 4 B D PROP . XVII . THEOR . Any two angles of a triangle are together less than ...
... manner , if the side BC be bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . A E 4 B D PROP . XVII . THEOR . Any two angles of a triangle are together less than ...
Página 22
... manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . B SCHOLIUM . ୯ This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest ...
... manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . B SCHOLIUM . ୯ This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest ...
Página 27
... manner it may be demonstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 30. Def . ) E B G C F D to one another . AB therefore is parallel to CD ...
... manner it may be demonstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 30. Def . ) E B G C F D to one another . AB therefore is parallel to CD ...
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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 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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 22 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.