A System of Popular Geometry: Containing in a Few Lessons So Much of the Elements of Euclid as is Necessary and Sufficient for a Right Understanding of Every Art and Science in Its Leading Truths and General Principles
Taylor and Walton, Booksellers to the University of London, 30 Upper Gower Street, 1836 - 128 páginas
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abcd adjacent angles altitudes angle abc angle bac angles eab angles equal base ac called centre chord circumference Consequently contained definition demonstration equal arches equal bases equal circles equal sides equal to cd equal to four equal triangles equally distant equi-angular finite right line Geometry given finite right given point given right line greater Hence ibid Join klmn Let abc line cd lines be drawn magnitude Note opposite angles parallel right lines parallel to ac parallelogram perpendicular Phob Plane Geometry Prob produced proportional right lines propositions quantities reciprocally proportional rect rectangle rectilineal figure respectively equal right line divided right line drawn right line intersect secant segments side ac square of cd submultiple supposition is false tangent theorem third side three sides tiples triangles abc unequal vertex
Página 33 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.
Página 3 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Página xxx - 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.
Página 32 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.
Página 27 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.
Página 101 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Página 53 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...
Página 12 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.