The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 Seiten |
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Seite 7
... polygons , by more than four straight lines . XXIV . Of three sided figures , an equilateral triangle is that which has three equal sides . An isosceles triangle is that which has only two sides equal . THE ELEMENTS OF EUCLID . BOOK I ...
... polygons , by more than four straight lines . XXIV . Of three sided figures , an equilateral triangle is that which has three equal sides . An isosceles triangle is that which has only two sides equal . THE ELEMENTS OF EUCLID . BOOK I ...
Seite 11
... polygons , by more than four straight lines . XXIV . Of three sided figures , an equilateral triangle is that which has three equal sides . An isosceles triangle is that which has only two sides equal . Book I. XXVI . A scalene triangle ...
... polygons , by more than four straight lines . XXIV . Of three sided figures , an equilateral triangle is that which has three equal sides . An isosceles triangle is that which has only two sides equal . Book I. XXVI . A scalene triangle ...
Seite 176
... polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is 176 THE ELEMENTS.
... polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is 176 THE ELEMENTS.
Seite 177
... polygons have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : and the po- lygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the homologous side FG ...
... polygons have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : and the po- lygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the homologous side FG ...
Seite 178
... polygon g 12. 5. 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 ...
... polygon g 12. 5. 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 ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram parallelogram AC perpendicular point F polygon prism proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Beliebte Passagen
Seite 28 - Any two sides of a triangle are together greater than the third side.
Seite 62 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 28 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Seite 57 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 26 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 163 - 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.
Seite 17 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 189 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Seite 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Seite 178 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.