Rudiments of plane geometry, including geometrical analysis, and plane trigonometry (Google eBook)

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Page 25 - The diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. It is obvious that all radii of the same circle are equal to each other and to a semidiameter. It likewise appears, from the slightest inspection, that a circle can have only one centre, and that circles are equal which have equal diameters.
Page 6 - Of quantities in a continued proportion, the first is said to have to the third, the duplicate ratio of what it has to the second ; to have to the fourth, a triplicate ratio; to the fifth, a quadruplicate ratio; and so forth, according to the number of ratios introduced between the extreme terms.
Page 97 - lines. 2. Straight lines are divided similarly, when their corresponding segments have the same ratio. 3. A straight line is said to be cut in extreme. and mean ratio, when the one segment is the mean proportional between the other segment and the whole line. 4.
Page 131 - PROB. To bisect a given triangle, by a straight line drawn from a given point in one of its sides. Let it be required, from the point D, to draw DF, bisecting the triangle ABC. ANALYSIS. If D be the middle of AC, the line DB drawn to the vertex will obviously
Page 9 - analogy are proportional by composition ; or the sum of the first and second is to the second, as the sum of the third and fourth to the fourth. Let A : B : : C : D, then by composition A + B : B : : C + D : D.
Page 9 - analogy are proportional by division; or the difference of the first and second is to the second, as the difference of the third and fourth to the fourth. Let A : B : : C : D; suppose A to be greater than B, then will C be greater than D
Page 179 - THEOR. In any triangle, the sum of two sides is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. In the triangle ABC, AB+AC : AB—AC
Page 70 - THEOR. The angle in a semicircle is a right angle, the angle in a greater segment is acute, and the angle in a smaller segment is obtuse. Let ABD be an angle in a semicircle, or standing on the
Page 61 - 2. The space included between an arc and its chord, is named a segment. 3. A sector is the portion of a circle contained by two radii and the arc lying between them. 4. The tangent to a circle is a straight line which touches the circumference, or meets it
Page 35 - Through a given point, to draw a straight line parallel to a given straight line. To draw, through the point C, a straight line parallel to AB.

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