## A course of practical geometry for mechanics |

### From inside the book

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**ratio**or proportion between F L and FK , shall be pre- cisely the same as that between FI and F H. Note as FL is to FI , so also is FK to FH ; and again , as F K is to F H , or as FL is to FI , so is KL to HI . EXAMPLES . 1. Reverse the ... Page 32

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**ratio**required ; for the lesser segment EB shall have the same proportion to the greater segment A E , as AE has to the sum of the two segments , A B. EXAMPLE . Divide a line 4 inches long into extreme and mean**ratio**. PROBLEM XXI . To ... Page 56

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**ratio**between the circumference and the diameter of a circle is yet undefined . PROBLEM LXXII . To make a circle equal to a triangle . 1. Make a rectangle equal to the given triangle . 2. Make a square equal to the rectangle . 3. On one ... Page 58

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**ratio**of the sector ADBA to the circle . 4. By Prob . XVI . cut off from either end of the base of the triangle the above**ratio**, ( in this case one - fourth . ) Draw a line to the vertex including this fourth , and the remaining three ... Page 60

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**ratio**of their homologous sides . " Duplicate**ratio**is the**ratio**of the square of one quantity to the square of another . EXAMPLES . 1. Make a square equal to the sum of three squares , whose sides are 1 , 2 , and 3 inches . 2. A circle ...### Other editions - View all

### Common terms and phrases

60 degrees altitude angle equal arc or angle Bisect called centre chords shall form circumference curvilineal cutting A B decagon describe a circle describe a regular describe an arc describe arcs cutting diagonals diameter dodecagon Draw a line Draw chords draw lines Draw the line ellipse equilateral triangle Euclid Euclid's Elements EXAMPLE generatrix geometry given angle given circle given line given point given right line given triangle gonals heptagon inches long inscribe isosceles triangle Join length Let A B line 2 inches line A B line parallel LVIII number of degrees number of equal parallel ruler parallelogram pentagon perpendicular plane point of intersection protractor radii radius ratio rectangle regular nonagon regular polygon rhombus right angles right-angled triangle segment square equal straight line superficies tangent trapezium triangle being given triangle equal triangle required vertex vertical angle Vide Def vide Prob

### Popular passages

Page 8 - A plane rectilineal angle is the inclination of two straight lines to one another, -which meet together, but are not in the same straight line.

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

Page 9 - CHG; and they are adjacent angles; but when a straight line standing on another straight line makes the adjacent angles equal to one another...

Page 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.

Page 13 - Of four-sided figures, a SQUARE is that which has all its sides equal, and all its angles right angles.

Page 9 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Page 14 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.

Page 8 - A plane angle is the inclination of two lines to one another* in a plane, which meet together, but are not in the same direction.

Page 13 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.

Page 8 - DBC, or CBD ; but, if there be only one angle at a point, it may be expressed by a letter placed at that point ; as the angle at E.