A Collection of Problems and Examples Adapted to the "Elementary Course of Mathematics.": With an Appendix Containing the Questions Proposed During the First Three Days of the Senate-House Examinations in the Years 1848, 1849, 1850, and 1851 |
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Page 54
... base AB ; and the difference of the segments of the base made by the perpendicular ; find the sides of the triangle . Given the vertical angle , the perpendicular let fall from the vertical angle on the base , and the rectangle under ...
... base AB ; and the difference of the segments of the base made by the perpendicular ; find the sides of the triangle . Given the vertical angle , the perpendicular let fall from the vertical angle on the base , and the rectangle under ...
Page 55
... triangle will be divided into six equal parts . 21. If a perpendicular be let fall from the vertex of any triangle on the base , the rectangle under the sides of the triangle is equal to the rectangle under the perpendi- TRIGONOMETRY . 55.
... triangle will be divided into six equal parts . 21. If a perpendicular be let fall from the vertex of any triangle on the base , the rectangle under the sides of the triangle is equal to the rectangle under the perpendi- TRIGONOMETRY . 55.
Page 56
... base , the vertical angle , and the differ- ence of the sides ; find the remaining angles . 30. The sides of a triangle are in arithmetical pro- gression , and its area is to that of an equilateral triangle of the same perimeter as 3 ...
... base , the vertical angle , and the differ- ence of the sides ; find the remaining angles . 30. The sides of a triangle are in arithmetical pro- gression , and its area is to that of an equilateral triangle of the same perimeter as 3 ...
Page 57
... base was measured of 2761 feet , and at either extremity of this base were taken the angles formed by the summit and the other extremity ; these were 58 ° 29 ′ and 111 ° 52 ′ ; also at the extremity from which the latter angle was taken ...
... base was measured of 2761 feet , and at either extremity of this base were taken the angles formed by the summit and the other extremity ; these were 58 ° 29 ′ and 111 ° 52 ′ ; also at the extremity from which the latter angle was taken ...
Page 58
... base AD of a feet , and observes the angle BDC ; he then advances to E , b feet further , and observes that the angle BEC the supplement of BDC . From these observations find the sides of the triangle . = 8. A person walking from C to D ...
... base AD of a feet , and observes the angle BDC ; he then advances to E , b feet further , and observes that the angle BEC the supplement of BDC . From these observations find the sides of the triangle . = 8. A person walking from C to D ...
Other editions - View all
A Collection of Problems and Examples, Adapted to the Elementary Course of ... Harvey Goodwin No preview available - 2019 |
A Collection of Problems and Examples Adapted to the 'Elementary Course of ... Harvey. Goodwin No preview available - 2015 |
A Collection of Problems and Examples, Adapted to the 'Elementary Course of ... Harvey Goodwin No preview available - 2010 |
Common terms and phrases
angular points arithmetical arithmetical mean arithmetical series axis base bisects centre of gravity chord circle concave convex lens cosē cosec curve cylinder Describe determine diameter direction distance Divide drawn elastic balls ellipse equal equation equilibrium feet find the height Find the number find the position Find the velocity fluid focal length force geometrical focus geometrical progression geometrical series given point given velocity given weight horizontal plane hyperbola immersed inches incident inclined plane inscribed latus rectum luminous point mirror motion moving Multiply observed parabola parallel parallelogram pencil of rays perpendicular placed pressure proportional prove pullies quantities radii radius ratio reflexion refracted respectively right angle shew sides sinē specific gravity sphere spherical square St John's College straight line string passing Subtract surface tangent tower triangle vertex
Popular passages
Page 111 - If two triangles have two sides of the one equal to two sides of the...
Page 128 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Page 111 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 112 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Page 144 - ... a circle. 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 160 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Page 112 - 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 160 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.