## Elements of Arithmetic, Algebra, and GeometryAdam Black and William Tait, 1826 |

### From inside the book

Results 1-5 of 19

Page 152

...

...

**angle BAC**is equal to the angle EDF ; where- fore , also the point C shall coincide with the point F , because the side AC is equal to the side DFs ; and because B coin- cides with E , and C with F , the side BC coincides with the side ... Page 155

...

...

**angle**ACD is greater than either of the interior and opposite**angles**CBA , CAB . Bisect AC in E , join BE , and ...**BAC**. In the same manner , if the side BC be bisected , it may be demonstrated that the**angle**BCG , that is , ACDe ... Page 156

...

...

**angle**CAB . greater than CB , cut off CD , equal to CB , and join BD . Then , because CD is equal to CB , the**angle**...**BAC**of the one , greater than the included**angle**EDF of the other , the base BC of that which has the greater ... Page 160

... angle CBD is equal to the two interior and opposite

... angle CBD is equal to the two interior and opposite

**angles BAC**, ACB , and the three interior angles of any triangle ABC , viz . ABC , BCA , CAB , are together equal to two right angles . C E Through the point B draw BE parallel to the ... Page 161

...

...

**angles**of the figure , together with four right**angles**; that is , the**angles**of the figure are equal to twice as many right**angles**, as the figure has sides wanting four . PROP . XIII . THEOREM . If two triangles ,**BAC**, EDF , have two ...### Other editions - View all

### Common terms and phrases

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

### Popular passages

Page 174 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Page 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.

Page 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...

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.