Elements of geometry and mensuration |
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Page 9
... half of a circle , bounded by the half of the circumference and the diameter joining its extremities . A quadrant is the quarter of a circle , or the half of a semi - circle , bounded by the fourth - part of the circum- ference and two ...
... half of a circle , bounded by the half of the circumference and the diameter joining its extremities . A quadrant is the quarter of a circle , or the half of a semi - circle , bounded by the fourth - part of the circum- ference and two ...
Page 12
... half of area ACD . Angles likewise are magnitudes which may be added , subtracted , & c . Thus , ACB + BCD LACD . And 4 BCD taken from ACD leaves 4 ACB . Also if LACB = BCD , then ‹ ACD is double of 4 ACB . QUESTIONS ON THE PRECEDING ...
... half of area ACD . Angles likewise are magnitudes which may be added , subtracted , & c . Thus , ACB + BCD LACD . And 4 BCD taken from ACD leaves 4 ACB . Also if LACB = BCD , then ‹ ACD is double of 4 ACB . QUESTIONS ON THE PRECEDING ...
Page 29
... half the parallelo- gram ABCD . Similarly the triangle FGH half the parallelogram EFGH . And the halves of equal things must themselves be equal ; .. the triangle BCD = the triangle FGH ; that is , all triangles upon the same , or equal ...
... half the parallelo- gram ABCD . Similarly the triangle FGH half the parallelogram EFGH . And the halves of equal things must themselves be equal ; .. the triangle BCD = the triangle FGH ; that is , all triangles upon the same , or equal ...
Page 37
... half the sum of all three sides of the same triangle . ( 13 ) Shew that the straight line drawn from the middle point of the base of an isosceles triangle to the vertex of the opposite angle is at right angles to the base , and bisects ...
... half the sum of all three sides of the same triangle . ( 13 ) Shew that the straight line drawn from the middle point of the base of an isosceles triangle to the vertex of the opposite angle is at right angles to the base , and bisects ...
Page 38
... half the hypothenuse . Is the ( 25 ) Explain what is meant by the square of a line . of the line AB the same as the square of the line BA ? square ( 26 ) Take the particular case of a right - angled tri- angle which is isosceles , and ...
... half the hypothenuse . Is the ( 25 ) Explain what is meant by the square of a line . of the line AB the same as the square of the line BA ? square ( 26 ) Take the particular case of a right - angled tri- angle which is isosceles , and ...
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Common terms and phrases
ABCDEF acres base bisect breadth centre chain chord circular circum circumference circumscribing circle compasses construction contained continued fraction curved decimal Diagonal Scale diagram diameter distance divided draw drawn edge equilateral triangle find the area find the length fraction frustum given angle given circle given line given point given straight line given triangle half height Hence hexagon inscribed instrument intersecting join Let ABCD lineal unit magnitude meet multiplied number of equal number of sides number of units opposite angle parallelogram perimeter perpendicular plane surface plot points of division PROB produced PROP proportional Protractor radii radius ratio rectangle rectangular regular polygon represent right angles shew shewn similar similar triangles square feet square foot square inches straight edge subtends suppose trapezium triangle ABC vernier vertex whole yards
Popular passages
Page 32 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 19 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 32 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.
Page 43 - 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 17 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 22 - Theorem. The greater side of every triangle is opposite to the greater angle. Let ABC be a triangle of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA. Because AC is greater than AB, make...
Page 192 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 126 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 20 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.