Elements of Arithmetic, Algebra, and GeometryAdam Black and William Tait, 1826 |
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Página 120
... opposite banks of a river , the breadth of which they wished to ascertain . A first shot the arrow across the river , and it flew 13 yards beyond the bank on which B stood . B then took it up , and from the place where it had fallen ...
... opposite banks of a river , the breadth of which they wished to ascertain . A first shot the arrow across the river , and it flew 13 yards beyond the bank on which B stood . B then took it up , and from the place where it had fallen ...
Página 149
... opposite sides equal to one an- other . XXX . - All other four sided figures besides these , are called Trapegiums . XXXI . - Straight lines , which are in the same plane , and being produced even so far both ways , do not meet , are ...
... opposite sides equal to one an- other . XXX . - All other four sided figures besides these , are called Trapegiums . XXXI . - Straight lines , which are in the same plane , and being produced even so far both ways , do not meet , are ...
Página 151
... angles equal , which are opposite to the equal sides . For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D , and the side AB lie along Book I the side DE ; then the point B OF GEOMETRY . 151.
... angles equal , which are opposite to the equal sides . For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D , and the side AB lie along Book I the side DE ; then the point B OF GEOMETRY . 151.
Página 152
... opposite to the equal sides AC and DF ; in the same manner , it appears that the angle ACB is equal to the angle DFE , and they are opposite to the equal sides AB and DE . Therefore , if two triangles , & c . Q. E. D. a Cons . b 2. 1 ...
... opposite to the equal sides AC and DF ; in the same manner , it appears that the angle ACB is equal to the angle DFE , and they are opposite to the equal sides AB and DE . Therefore , if two triangles , & c . Q. E. D. a Cons . b 2. 1 ...
Página 153
... opposite , viz . the angle CAB equal to FDE , and CBA to FED . Therefore , if two triangles , & c . Q. E. D. Cor . 1. The straight line drawn from the vertex of an isosceles triangle , so as to bisect the base , is perpendicular to it ...
... opposite , viz . the angle CAB equal to FDE , and CBA to FED . Therefore , if two triangles , & c . Q. E. D. Cor . 1. The straight line drawn from the vertex of an isosceles triangle , so as to bisect the base , is perpendicular to it ...
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Términos y frases comunes
algebraic quantities angle ABC angle ACB angle BAC angle CAB angle EBA annex Arithmetic binomial Binomial Theorem bisected Book centre ciphers circumference coefficient consequently continued fraction cube root denominator diameter difference divided dividend divisor drawn equation example expressed exterior angle figure find the values fore fourth given circle given number greater greatest common measure guinea Hence improper fraction join least common multiple less manner merator minuend multiplied number of terms opposite angles parallel parallelogram perpendicular preceding prefixed PROP Q. E. D. Cor quotient ratio Reduce remaining angle Required the sum right angles rule Scholium sides square root straight line subtracted subtrahend surd tangent THEOREM third Transp triangle ABC units unity unknown quantity vulgar fraction Wherefore whole angle whole number
Pasajes populares
Página 174 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 132 - 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 172 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...
Página 171 - 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 129 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other.
Página 171 - C to the remaining angle at F. For, if the angles ABC, DEF be not equal, one of them is greater than the other : Let ABC be the greater, and at the point B, in the straight line AB, make the angle ABG equal to the angle (23.
Página 164 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on GEOMETRY.
Página 142 - EK, because EH is less than EK ; therefore the square of BH is greater than the square of FK, and the straight line BH greater than FK, and therefore BC is greater than FG.
Página 109 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Página 148 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two ; and when the adjacent angles are equal, they ate right angles.