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, 1849 - 317 páginas |
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Página 17
... divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide ...
... divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide ...
Página 30
... divided into as many trian- gles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are equal to twice as ...
... divided into as many trian- gles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are equal to twice as ...
Página 32
... divided into four triangles , which contain eight right angles ; that is , as many times two right an- gles as there are units in the number of sides diminished by two . But to avoid all ambiguity , we shall henceforth limit our ...
... divided into four triangles , which contain eight right angles ; that is , as many times two right an- gles as there are units in the number of sides diminished by two . But to avoid all ambiguity , we shall henceforth limit our ...
Página 49
... divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let ...
... divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let ...
Página 50
... divided into any two parts , the square of the whole line is equal to the squares of the two parts , together with twice the rectangle con- tained by the parts . Let the straight line AB be divided into any two parts in C ; the square ...
... divided into any two parts , the square of the whole line is equal to the squares of the two parts , together with twice the rectangle con- tained by the parts . Let the straight line AB be divided into any two parts in C ; the square ...
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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 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 149 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
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 on the line between the points of section, is equal to the square on 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 52 - 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 9 - 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 296 - 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.
Página 15 - 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.
Página 283 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página 22 - Any two sides of a triangle are together greater than the third side.
Página 26 - ... sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.