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 PrinciplesTaylor and Walton, Booksellers to the University of London, 30 Upper Gower Street, 1836 - 128 páginas |
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Página xxv
... equal . And one right line is said to be farther from the centre than an ... respect to the given point , 51 . DEF . XXIII . A rectilineal figure is said ... equals another magni- tude added to itself an integral number of times , the ...
... equal . And one right line is said to be farther from the centre than an ... respect to the given point , 51 . DEF . XXIII . A rectilineal figure is said ... equals another magni- tude added to itself an integral number of times , the ...
Página xxvi
... equal to an angle in the other , they are called equi - angular parallelo ... respectively to two adjacent sides of the parallelogram , so as to make four ... equal , 5 . Ax . 3. Things which are equal to the same thing are equal to each ...
... equal to an angle in the other , they are called equi - angular parallelo ... respectively to two adjacent sides of the parallelogram , so as to make four ... equal , 5 . Ax . 3. Things which are equal to the same thing are equal to each ...
Página xxvii
... equal , respectively , to all the sides of the other , then the angles , which in these triangles are opposite to equal , sides , are also equal , ibid . ART . 7. Such triangles as are described in the preceding Article are equal , in every ...
... equal , respectively , to all the sides of the other , then the angles , which in these triangles are opposite to equal , sides , are also equal , ibid . ART . 7. Such triangles as are described in the preceding Article are equal , in every ...
Página xxviii
... equal bases and between the same parallels are equal , ibid . ART . 27. Equal triangles upon the same base , and ... respectively to two angles in the other , the third angle of the one is also equal to the third angle of the other , 30 ...
... equal bases and between the same parallels are equal , ibid . ART . 27. Equal triangles upon the same base , and ... respectively to two angles in the other , the third angle of the one is also equal to the third angle of the other , 30 ...
Página xxxii
... respectively equal to the angles of another , the three sides of one triangle have to the corresponding sides of the other , respectively , the same ratio , ibid . ART . 113. If the three sides of any triangle have respectively to the ...
... respectively equal to the angles of another , the three sides of one triangle have to the corresponding sides of the other , respectively , the same ratio , ibid . ART . 113. If the three sides of any triangle have respectively to the ...
Términos y frases comunes
ABCD altitudes angle ABC angle BAC angle CDA angles EAB angles equal base AC 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 Euclid finite right line Geometry given finite right given point given right line greater Hence ibid internal angles Join KLMN Let ABC line CD lines be drawn magnitude NOTE opposite angles parallel right lines parallelogram perpendicular PROB produced propositions quantities reciprocally proportional rectangle rectilineal figure respectively equal right angles right line divided right line drawn right line intersect segments side AB side AC square of AB square of AC submultiple supposition is false tangent theorem third side three sides tiples triangle ABC unequal vertex
Pasajes populares
Página 31 - 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 xxxi - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
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 30 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.
Página 25 - 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 99 - 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 51 - 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 10 - 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.
Página 11 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.