## Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and Illustrations |

### From inside the book

Page 142

... the same antecedents as the former , and the same

... the same antecedents as the former , and the same

**consequents**as the latter . :**Let**A B C :**D**, and**B**:**E**::**D**: F ; then A :**E**::**C**: F. For , alternating both analogies , A :**C**::**B**:**D**, and 1**B**:**D**::**E**: F ; whence 142 ELEMENTS OF ... Page 144

... one antecedent is to its

... one antecedent is to its

**consequent**, so is the**sum of all**the antecedents**to the sum of all**the conse- quents . : :**Let**A B C :**D**::**E**: F :: G : H ; then A :**B**:: A +**C**+**E**+ G :**B**+**D**+ F + H . Because A :**B**::**C**:**D**, ( V. 6. ) AD =**BC**... Page 422

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...

**every**34 miles of perpendicular ascent . At 7 miles in height , the ...**AB**, AC ...**c**. ;**BC**+**CD**+**DE**, &**c**. or BH .**Let**n denote the number of sec- tions or strata contained in the mass of air , and (**AB**+ AH ) N 2 will nearly express the ...### Contents

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### Common terms and phrases

ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore

### Popular passages

Page 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Page 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...

Page 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Page 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.

Page 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.

Page 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...

Page 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.

Page 38 - 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 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.