The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 155
... SOLID is that which hath length , breadth and thickness . II . That which bounds a solid is a superficies . III . A ... angle con- tained by that straight line , and another drawn from the point in which the first line meets the ...
... SOLID is that which hath length , breadth and thickness . II . That which bounds a solid is a superficies . III . A ... angle con- tained by that straight line , and another drawn from the point in which the first line meets the ...
Página 156
... solid angle is that which is made by the meeting of more than two plane angles , which are not in the same plane , in one point . * Χ . • The tenth definition is omitted for reasons given in the notes . * ΧΙ . Similar solid figures are ...
... solid angle is that which is made by the meeting of more than two plane angles , which are not in the same plane , in one point . * Χ . • The tenth definition is omitted for reasons given in the notes . * ΧΙ . Similar solid figures are ...
Página 168
... solid angle be contained by three plane angles , any two of them are greater than the third . * Let the solid angle at A be contained by the three plane angles , BAC , CAD , DAB . Any two of them are greater than the third . If the ...
... solid angle be contained by three plane angles , any two of them are greater than the third . * Let the solid angle at A be contained by the three plane angles , BAC , CAD , DAB . Any two of them are greater than the third . If the ...
Página 169
... angle DAB is equal to the angle EAB : therefore the base DB is equal ( 4. 1. ) to the base BE . And because BD , DC are great- er ( 20. 1. ) than CB , and one of them , BD ... solid angle is contained by plane angles which together ...
... angle DAB is equal to the angle EAB : therefore the base DB is equal ( 4. 1. ) to the base BE . And because BD , DC are great- er ( 20. 1. ) than CB , and one of them , BD ... solid angle is contained by plane angles which together ...
Página 170
... solid angle at B is contained by three plane angles CBA , ABF , FBC , of which any two are greater ( 20.11 . ) than the third , the angles CBA , ABF , are greater than the angle FBC : for the same reason , the two plane angles at each ...
... solid angle at B is contained by three plane angles CBA , ABF , FBC , of which any two are greater ( 20.11 . ) than the third , the angles CBA , ABF , are greater than the angle FBC : for the same reason , the two plane angles at each ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 36 - 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 145 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 65 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 248 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 121 - 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 21 - 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 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Página 80 - 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. either the sides adjacent to the equal...
Página 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.