The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 páginas |
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Página 17
... half of DE , and the line joining either of their points of intersection with A will bisect the given angle . It is plain , that if the radius be taken equal to AD or AE , A must be joined with the remote point of intersection , as A ...
... half of DE , and the line joining either of their points of intersection with A will bisect the given angle . It is plain , that if the radius be taken equal to AD or AE , A must be joined with the remote point of intersection , as A ...
Página 18
... half of FE , and joining their point of intersection with C. The 12th proposition would be better placed after the 16th ; as we cannot prove without the assistance of the 16th that there can be but one perpendicular drawn to a straight ...
... half of FE , and joining their point of intersection with C. The 12th proposition would be better placed after the 16th ; as we cannot prove without the assistance of the 16th that there can be but one perpendicular drawn to a straight ...
Página 23
... half of BAC ; and there- fore ( I. 19. ) each segment of BC is less than the adjacent side . This proposition is never referred to by Euclid , except in the 8th proposition of the third book ; and that proposition may be proved without ...
... half of BAC ; and there- fore ( I. 19. ) each segment of BC is less than the adjacent side . This proposition is never referred to by Euclid , except in the 8th proposition of the third book ; and that proposition may be proved without ...
Página 33
... half a right angle . Cor . 5. If two angles of one triangle be equal to two angles of another , their remaining angles are equal . Cor . 6. Each angle of an equilateral triangle is one third of two right angles , or two thirds of one ...
... half a right angle . Cor . 5. If two angles of one triangle be equal to two angles of another , their remaining angles are equal . Cor . 6. Each angle of an equilateral triangle is one third of two right angles , or two thirds of one ...
Página 37
... half of the parallelogram EC , because ( I. 34. ) the diagonal AB bisects it ; and the triangle DBC is the half of the parallelo- gram BF , because the diagonal DC bisects it : but ( I. ax . 7. ) the halves of equals are equal ...
... half of the parallelogram EC , because ( I. 34. ) the diagonal AB bisects it ; and the triangle DBC is the half of the parallelo- gram BF , because the diagonal DC bisects it : but ( I. ax . 7. ) the halves of equals are equal ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Pasajes populares
Página 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 143 - 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.
Página 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Página 57 - 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 on the other part.
Página 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Página 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 32 - 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 sides.
Página 40 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...