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 TrigonometryW. E. Dean, 1847 - 317 páginas |
Dentro del libro
Resultados 1-5 de 66
Página 12
... fore CA is equal to CB ; wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight ...
... fore CA is equal to CB ; wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight ...
Página 17
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . D E F B C SCHOLIUM . By the same construction , each of the halves BAF , CAF , may be divi- ded into two equal parts ; and thus , by successive subdivisions ...
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . D E F B C SCHOLIUM . By the same construction , each of the halves BAF , CAF , may be divi- ded into two equal parts ; and thus , by successive subdivisions ...
Página 33
... fore the opposite sides and angles of a parallelogram are equal to one an- other ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ...
... fore the opposite sides and angles of a parallelogram are equal to one an- other ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ...
Página 35
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA E B A D F is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; but the triangle ABC is the half of the ...
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA E B A D F is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; but the triangle ABC is the half of the ...
Página 36
... fore parallel to it . PROP . XL . THEOR . B Equal triangles on the same side of bases which are equal and in the same straight line , are between the same parallels . Let the equal triangles ABC , DEF be upon equal bases BC , EF , in ...
... fore parallel to it . PROP . XL . THEOR . B Equal triangles on the same side of bases which are equal and in the same straight line , are between the same parallels . Let the equal triangles ABC , DEF be upon equal bases BC , EF , in ...
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 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 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
Pasajes populares
Página 53 - 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 18 - If two triangles have two sides of the one equal to two sides of the...
Página 54 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 82 - 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 31 - 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 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 21 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Página 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Página 298 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.