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 |
Dentro del libro
Resultados 1-5 de 100
Página 9
... angle at E. ' 7. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a ...
... angle at E. ' 7. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a ...
Página 10
... right angled triangle is that which has a right angle . 23. An obtuse angled triangle is that which has an obtuse angle . 24. An acute angled triangle is that which has three acute angles . 25 of four sided figures , a square is that ...
... right angled triangle is that which has a right angle . 23. An obtuse angled triangle is that which has an obtuse angle . 24. An acute angled triangle is that which has three acute angles . 25 of four sided figures , a square is that ...
Página 18
... right angles to a given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi red to draw a straight line from the point C at right angles to AB . F Take any point D ...
... right angles to a given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi red to draw a straight line from the point C at right angles to AB . F Take any point D ...
Página 19
... right angles , or are together equal to two right angles . For , if the angle CBA be equal to ABD , each of them is a right angle ( Def . 7. ) ; but , if not , from the point B draw BE at right angles ( 11. 1. ) A E A D B D B C to CD ...
... right angles , or are together equal to two right angles . For , if the angle CBA be equal to ABD , each of them is a right angle ( Def . 7. ) ; but , if not , from the point B draw BE at right angles ( 11. 1. ) A E A D B D B C to CD ...
Página 20
... right angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax ...
... right angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax ...
Otras ediciones - Ver todas
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.