Modern geometry [ed.] with an appendix by W.B. Jack1876 |
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Página 134
... Length . Corresponding Units of Surface . Inch Square inch . Foot Square ... length . A surface equivalent to twelve squares with sides I foot long ... rectangle as there are units of length in the other side . Hence the number ...
... Length . Corresponding Units of Surface . Inch Square inch . Foot Square ... length . A surface equivalent to twelve squares with sides I foot long ... rectangle as there are units of length in the other side . Hence the number ...
Página 140
... rectangle whose base is half the perimeter and whose height is the perpen ... rectangle having the side for base and the radius for height ; dand ... contained by half the circumference and the radius , or the area of a circle ...
... rectangle whose base is half the perimeter and whose height is the perpen ... rectangle having the side for base and the radius for height ; dand ... contained by half the circumference and the radius , or the area of a circle ...
Página 142
... rectangle AEFC ; then A E F C is the rectangle contained by the sum and difference of Construct the square A B H G on A B , and draw D L parallel to A G ; then K H is the square on B C , and E L , DO , B F are equal rectangles . Now the ...
... rectangle AEFC ; then A E F C is the rectangle contained by the sum and difference of Construct the square A B H G on A B , and draw D L parallel to A G ; then K H is the square on B C , and E L , DO , B F are equal rectangles . Now the ...
Página 143
... rectangle contained by A C , C B. B H L F E K But A B E D , the square on A B , is made up of these four figures , therefore the square on A B is equal to the squares on AC , C B , and twice the rectangle contained by A C , CB . THEOREM ...
... rectangle contained by A C , C B. B H L F E K But A B E D , the square on A B , is made up of these four figures , therefore the square on A B is equal to the squares on AC , C B , and twice the rectangle contained by A C , CB . THEOREM ...
Página 144
... rectangle contained by the two unequal parts , together with the square on the part between the points of section . Let A B be the line , bisected in C and divided into unequal parts in D. A C D B G K L F H Let C BEF be the square on CB ...
... rectangle contained by the two unequal parts , together with the square on the part between the points of section . Let A B be the line , bisected in C and divided into unequal parts in D. A C D B G K L F H Let C BEF be the square on CB ...
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Modern Geometry [Ed.] with an Appendix by W.B. Jack Richard Wormell Sin vista previa disponible - 2016 |
Términos y frases comunes
A B and C D A B C D adjacent angles alternate angles angles equal angular points base bisector centre chord circumference circumscribing circle Construct a triangle contra-positive converse decagon describe a circle diameter distance divided draw a straight extremities figure fixed point fulfils the given given angle given circle given condition given straight line gonals greater Hence hypothenuse inches inscribed inscribed angle inscribed circle interior angles isosceles triangle less Let A B C line A B locus of points magnitudes middle points number of sides opposite angles opposite sides parallel parallelogram perpendicular point of contact point of intersection PROBLEM propositions proved quadrilateral ratio rect rectangle contained regular polygon respectively equal rhombus right angles right-angled triangle segment semicircle side opposite square on A B tangent termed Theo THEOREMS ON CHAPTER triangles are equal vertical angle
Pasajes populares
Página 242 - 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 240 - If a straight line be divided into any two parts, four 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.
Página 240 - 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.
Página 242 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Página 242 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Página 241 - If the first has to the second the same ratio which the third has to the fourth...
Página 240 - 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 242 - 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 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 239 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.