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 TrigonometryCollins and Hannay, 1833 - 333 σελίδες |
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Αποτελέσματα 1 - 5 από τα 22.
Σελίδα 19
... polygons , by more than four straight lines . XIX . Of three sided figures , an equilateral triangle is that which has three equal sides . XX . An isosceles triangle is that which has only two sides equal . AAA XXI . A scalene triangle ...
... polygons , by more than four straight lines . XIX . Of three sided figures , an equilateral triangle is that which has three equal sides . XX . An isosceles triangle is that which has only two sides equal . AAA XXI . A scalene triangle ...
Σελίδα 141
... polygons have ; and the polygon ABCDE has to the polygon FGHKL a ratio duplicate of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is simi- lar to the polygon FGHKL , the angle BAE is ...
... polygons have ; and the polygon ABCDE has to the polygon FGHKL a ratio duplicate of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is simi- lar to the polygon FGHKL , the angle BAE is ...
Σελίδα 142
... polygon ABCDE to the polygon FGHKL : but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the side AB has to the homologous side FG . Therefore also the polygon ABCDE has to the polygon FGHKL the duplicate ...
... polygon ABCDE to the polygon FGHKL : but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the side AB has to the homologous side FG . Therefore also the polygon ABCDE has to the polygon FGHKL the duplicate ...
Σελίδα 161
... polygon inscribed in a circle is less than the circumference of the circle . COR . 2. If from a point two straight lines be drawn touching a cir . cle , these two lines are together greater than the arch intercepted be tween them ; and ...
... polygon inscribed in a circle is less than the circumference of the circle . COR . 2. If from a point two straight lines be drawn touching a cir . cle , these two lines are together greater than the arch intercepted be tween them ; and ...
Σελίδα 162
... polygons , of the same number of sides , inscribed in circles , are similar , and are to one another as the squares of the diameters of the circles . Let ABCDEF and GHIKLM be two equilateral polygons of the same number of sides ...
... polygons , of the same number of sides , inscribed in circles , are similar , and are to one another as the squares of the diameters of the circles . Let ABCDEF and GHIKLM be two equilateral polygons of the same number of sides ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 49 - PROB. jf 0 a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle, Let AB be the given straight line, and C the given triangle, and D the given rectilineal angle.
Σελίδα 29 - The angles which one straight line makes with another upon one tide 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.
Σελίδα 19 - 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.
Σελίδα 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 90 - 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.
Σελίδα 86 - 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.
Σελίδα 87 - 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 touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 43 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Σελίδα 39 - Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. If a straight line fall upon two parallel straight lines, it makes the alter' male angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same. side together equal to two right angles.
Σελίδα 54 - If there be two straight lines, one of which is 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...