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 σελίδες |
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Σελίδα xxiii
... opposite pair are called Vertically opposite angles , 16 . DEF . IX . Two right lines are said to be equally distant from one another when any two points whatsoever in the one not the greater , and any two equally remote points in the ...
... opposite pair are called Vertically opposite angles , 16 . DEF . IX . Two right lines are said to be equally distant from one another when any two points whatsoever in the one not the greater , and any two equally remote points in the ...
Σελίδα xxiv
... opposite pair of points towards the same hand are equal to each other , 16 . DEF . X. Parallel right lines are those which are equally distant from each other , 17 . DEF . XI . A parallelogram is a four - sided rectilineal figure , each ...
... opposite pair of points towards the same hand are equal to each other , 16 . DEF . X. Parallel right lines are those which are equally distant from each other , 17 . DEF . XI . A parallelogram is a four - sided rectilineal figure , each ...
Σελίδα xxvi
... at the bases which are opposite to equal sides , are respectively equal , 5 . ART . 3. Such triangles as above described are equal , in every respect , to each other , ibid . ART . 4. A triangle which has two of its xxvi.
... at the bases which are opposite to equal sides , are respectively equal , 5 . ART . 3. Such triangles as above described are equal , in every respect , to each other , ibid . ART . 4. A triangle which has two of its xxvi.
Σελίδα xxvii
... opposite the equal sides , equal , 8 . ART . 5. A triangle which has two of its angles equal , has also its sides opposite the equal angles equal , 9 . ART . 6. If there be two triangles which have all the sides of the one equal ...
... opposite the equal sides , equal , 8 . ART . 5. A triangle which has two of its angles equal , has also its sides opposite the equal angles equal , 9 . ART . 6. If there be two triangles which have all the sides of the one equal ...
Σελίδα xxviii
... opposite to that greater side is greater than the angle opposite to the lesser , ibid . ART . 42. In any triangle , if one angle be greater than another , the side opposite to that greater side is greater than the side opposite to the ...
... opposite to that greater side is greater than the angle opposite to the lesser , ibid . ART . 42. In any triangle , if one angle be greater than another , the side opposite to that greater side is greater than the side opposite to the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 30 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.