## Euclid's Elements of geometry, the first three books (the fourth, fifth, and sixth books) tr. from the Lat. To which is added, A compendium of algebra (A compendium of trigonometry). |

### From inside the book

Page 202

If two triangles ( ABC and DEF )

If two triangles ( ABC and DEF )

**have one angle of the one equal to one angle of the other**, ( A to D ) and the sides about the equal angles proportional ( BA to AC as ED to DF ) , the triangles will be equiangular ; and will have the ... Page 203

If two triangles ( ABC , DEF ) ,

If two triangles ( ABC , DEF ) ,

**have one angle of the one equal to one angle of the other**( B to E ) , and the sides about two of the remaining angles proportional ( BA to AC , as ED to DF ) , but the two remaining angles ( C and F ) ... Page 218

Triangles which

Triangles which

**have one angle of the one equal to one angle of the other**, are to each other in a ratio compounded of the ratios of the sides about the equal angles . Cor . 3. - Any parallelograms or triangles are to one another in a ...### What people are saying - Write a review

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### Common terms and phrases

absurd added appears arch assumed base becomes bisected Book called centre circle circumference co-efficient common Const construct contained oftener describe difference divided double draw drawn equal angles equal by Hypoth equal by Prop equation equi-submultiples equiangular equilateral evident example extremity fall figure fore fourth fraction given line given right line greater half Hypoth indices inscribed internal less means meet multiplied namely opposite parallel parallelogram pass perpendicular possible PROBLEM produced proportional PROPOSITION quantities ratio rectangle rectilineal figure remaining right angles root RULE segment side AC similar similarly similarly demonstrated squares of AC stand submultiple subtract taken term THEOREM third touches triangle BAC twice the rectangle whole

### Popular passages

Page 20 - If two triangles have two sides of the one equal to two sides of the...

Page 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Page 209 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.

Page 218 - 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 114 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.

Page 90 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Page 129 - In any proportion, the product of the means is equal to the product of the extremes.

Page 163 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.

Page 215 - ... are to one another in the duplicate ratio of their homologous sides.

Page 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.