Elements of Arithmetic, Algebra, and GeometryAdam Black and William Tait, 1826 |
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Side 146
... angle at E. - VII . When a straight line AB , standing on another straight line CD , makes the adjacent angles ABC and ABD equal to one another , each of the angles is called a right angle , and the straight line , which stands on the ...
... angle at E. - VII . When a straight line AB , standing on another straight line CD , makes the adjacent angles ABC and ABD equal to one another , each of the angles is called a right angle , and the straight line , which stands on the ...
Side 147
... angles , or are , together , equal to two right angles . For , if AB be perpendicular to CD , then each of the angles ABC , ABD , is a right angle ; and , therefore , are , together , equal to two right angles . But , if one of them ...
... angles , or are , together , equal to two right angles . For , if AB be perpendicular to CD , then each of the angles ABC , ABD , is a right angle ; and , therefore , are , together , equal to two right angles . But , if one of them ...
Side 149
... angles . Book I. XXVI . Of four sided figures , a square is that which has all its sides equal , and all its angles right angles . XXVII . - An oblong , is that which has all its angles right angles , but has not all its sides equal ...
... angles . Book I. XXVI . Of four sided figures , a square is that which has all its sides equal , and all its angles right angles . XXVII . - An oblong , is that which has all its angles right angles , but has not all its sides equal ...
Side 150
... right angles are equal to one another . XI . Two straight lines , which intersect one another , cannot be both parallel to the same straight line . XII . The shortest distance between two points is a straight line . Cor . Any two sides ...
... right angles are equal to one another . XI . Two straight lines , which intersect one another , cannot be both parallel to the same straight line . XII . The shortest distance between two points is a straight line . Cor . Any two sides ...
Side 152
... angles ABC and ACB op- posite to the equal sides AC and AB are equal . A For , let the straight line AD bisect or ... right angles . Cor . 4. If the equal sides AB and AC be produced to E and F , the angles EBC and BCF on the other side ...
... angles ABC and ACB op- posite to the equal sides AC and AB are equal . A For , let the straight line AD bisect or ... right angles . Cor . 4. If the equal sides AB and AC be produced to E and F , the angles EBC and BCF on the other side ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 174 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.