A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for ExerciseG. B. Whittaker, 1825 - 372 páginas |
Dentro del libro
Resultados 1-5 de 55
Página xvi
... rectangle , under the ordinate and abscissa of a parabola , was a limit always greater than the inscribed rectilineal figure , and less than the circumscribed . In some other curves , a similar conclusion was found , and Archimedes ...
... rectangle , under the ordinate and abscissa of a parabola , was a limit always greater than the inscribed rectilineal figure , and less than the circumscribed . In some other curves , a similar conclusion was found , and Archimedes ...
Página 189
... 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 . Let A and BC be two straight lines ; and let BC be divided into any parts in 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 . Let A and BC be two straight lines ; and let BC be divided into any parts in the ...
Página 190
... rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , and by A , DE and also by A ... rectangle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square of AB . D F E ...
... rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , and by A , DE and also by A ... rectangle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square of AB . D F E ...
Página 191
... rectangle contained by AC , CB . C B G K Upon AB describe ( 46. 1. ) the square ADEB , and join BD , and through C ... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ...
... rectangle contained by AC , CB . C B G K Upon AB describe ( 46. 1. ) the square ADEB , and join BD , and through C ... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ...
Página 192
... rectangle contained by AD , DB , for DH is equal ( Cor . 4. 2 ) to DB ; and DF together with CH is the gnomon CMG ; therefore the gnomon CMG , is equal to the rectangle AD , DB : To each of these add LG , which is equal ( Cor . 4. 2 ...
... rectangle contained by AD , DB , for DH is equal ( Cor . 4. 2 ) to DB ; and DF together with CH is the gnomon CMG ; therefore the gnomon CMG , is equal to the rectangle AD , DB : To each of these add LG , which is equal ( Cor . 4. 2 ...
Contenido
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709 | |
Términos y frases comunes
ABC is equal altitude angle ABC angle BAC axis bisected centre circle ABCD circumference co-efficient cone conic section convergency curve cylinder described diameter divided draw equal angles equation equiangular equimultiples factors fluxion fore fraction geometrical progression given straight line gnomon greater Hence hyperbola join less Let ABC magnitudes multiple opposite parabola parallel parallelogram perpendicular plane angles polygon prism produced proportional pyramid Q. E. D. PROP Q. E. D. Proposition radius rectangle rectangle contained rectilineal figure remaining angle right angles segment shewn side BC similar sine solid angle solid parallelopiped spherical triangle square of AC subtract surd tang tangent Theorem third tiple triangle ABC vertex whence Wherefore
Pasajes populares
Página 172 - 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...
Página 191 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 190 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 196 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Página 192 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 177 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Página 286 - 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 179 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.