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 |
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Página 10
... polygons , by more than four straight lines . 19. Of three sided figures , an equilateral triangle is that which has three equal sides . 20. An isosceles triangle is that which has only two sides equal . AAA 21. A scalene triangle is ...
... polygons , by more than four straight lines . 19. Of three sided figures , an equilateral triangle is that which has three equal sides . 20. An isosceles triangle is that which has only two sides equal . AAA 21. A scalene triangle is ...
Página 31
... right angle . SCHOLIUM . When ( Cor . 1. ) is applied to polygons , which have re - entrant angles , as ABC each re - entrant angle must be regarded as greater than two right angles . And , by joining BD , BE , BF , OF GEOMETRY . BOOK I.
... right angle . SCHOLIUM . When ( Cor . 1. ) is applied to polygons , which have re - entrant angles , as ABC each re - entrant angle must be regarded as greater than two right angles . And , by joining BD , BE , BF , OF GEOMETRY . BOOK I.
Página 32
... polygons with salient angles , which might otherwise be named convex polygons . Every convex polygon is such that a straight line , drawn at pleasure , cannot meet the contour of the polygon in more than two points . A PROP . XXXIII ...
... polygons with salient angles , which might otherwise be named convex polygons . Every convex polygon is such that a straight line , drawn at pleasure , cannot meet the contour of the polygon in more than two points . A PROP . XXXIII ...
Página 45
... polygon ABCDE will be equivalent to the polygon ABCF , which has one side less than the original polygon . For the triangles CDE , CFE , have the base ČE common , and they are between the same paral- lels ; since their vertices D , F ...
... polygon ABCDE will be equivalent to the polygon ABCF , which has one side less than the original polygon . For the triangles CDE , CFE , have the base ČE common , and they are between the same paral- lels ; since their vertices D , F ...
Página 46
... polygon ; for , by suc- cessively diminishing the number of its sides , one , being retrenched at each step of the process , the equivalent triangle will at length be found . COR . Since a triangle may be converted into an equivalent ...
... polygon ; for , by suc- cessively diminishing the number of its sides , one , being retrenched at each step of the process , the equivalent triangle will at length be found . COR . Since a triangle may be converted into an equivalent ...
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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 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.