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 TrigonometryG. Long, 1819 - 333 pagine |
Dall'interno del libro
Risultati 1-5 di 22
Pagina 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 . Δ Δ Δ XXI . A scalene ...
... 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 . Δ Δ Δ XXI . A scalene ...
Pagina 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 ...
... 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 ...
Pagina 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 ra ...
... 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 ra ...
Pagina 161
... polygon inscribed in a circle is less than the circumference of the circle . COR . 2. If from a point two straight lines be drawntouching a circle , these two lines are together greater than the arch intercepted between them ; and hence ...
... polygon inscribed in a circle is less than the circumference of the circle . COR . 2. If from a point two straight lines be drawntouching a circle , these two lines are together greater than the arch intercepted between them ; and hence ...
Pagina 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 ...
Altre edizioni - Visualizza tutto
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Visualizzazione completa - 1819 |
Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Visualizzazione completa - 1837 |
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Visualizzazione completa - 1854 |
Parole e frasi comuni
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 and similar 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 proportionals 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 parallelepipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Brani popolari
Pagina 56 - 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.
Pagina 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.
Pagina 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Pagina 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Pagina 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Pagina 130 - 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.
Pagina 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Pagina 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Pagina 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Pagina 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.