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, 1837 - 318 sider |
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Side 13
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
Side 14
... base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
... base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
Side 15
... base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
... base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
Side 16
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Side 17
... base EF , and upon side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but ...
... base EF , and upon side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but ...
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Vanlige uttrykk og setninger
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 spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 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.
Side 12 - AB; but things which are equal to the same are equal to one another...
Side 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.
Side 288 - 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.
Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.
Side 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Side 127 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 23 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Side 19 - 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 are either two 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.