An Elementary Geometry and Trigonometry |
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... figure is constructed as the proof will require . A sixth Book of Problems of Construction is added , which is followed by Problems for the pupil to solve . This Book , or any part of it , if thought best , can be taken immediately ...
... figure is constructed as the proof will require . A sixth Book of Problems of Construction is added , which is followed by Problems for the pupil to solve . This Book , or any part of it , if thought best , can be taken immediately ...
Page 5
... it may be proved that AED CEB D E C B * The figures alone refer to an article in the same Book ; in referring to an article in another Book the number of the Book is prefixed . PLANE GEOMETRY . THEOREM IV . 12. Two angles whose BOOK I. 5.
... it may be proved that AED CEB D E C B * The figures alone refer to an article in the same Book ; in referring to an article in another Book the number of the Book is prefixed . PLANE GEOMETRY . THEOREM IV . 12. Two angles whose BOOK I. 5.
Page 8
... FIGURES . DEFINITIONS . 19. A Plane Figure is a portion of a plane bounded by lines either straight or curved . When the bounding lines are straight , the figure is a polygon , and the sum of the bounding lines is the perimeter . 20. An ...
... FIGURES . DEFINITIONS . 19. A Plane Figure is a portion of a plane bounded by lines either straight or curved . When the bounding lines are straight , the figure is a polygon , and the sum of the bounding lines is the perimeter . 20. An ...
Page 18
... figure is a parallelogram . Let ABCD be a quadrilateral having BC equal and parallel to AD ; then ABCD is a parallelogram . A C B D_ Draw the diagonal BD . As BC is parallel to AD , the alternate angles CBD and BDA are equal ( 17 ) ...
... figure is a parallelogram . Let ABCD be a quadrilateral having BC equal and parallel to AD ; then ABCD is a parallelogram . A C B D_ Draw the diagonal BD . As BC is parallel to AD , the alternate angles CBD and BDA are equal ( 17 ) ...
Page 20
... figure has sides minus two . F C B E D For if from any vertex A , diagonals A C , AD , AE , are drawn , the polygon will be divided into as many triangles as it has sides minus two ; and the sum of the angles of each triangle is equal ...
... figure has sides minus two . F C B E D For if from any vertex A , diagonals A C , AD , AE , are drawn , the polygon will be divided into as many triangles as it has sides minus two ; and the sum of the angles of each triangle is equal ...
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Common terms and phrases
A B C ABCDEF acute angle adjacent altitude angle BCD apothem arc or angle bisect centre chord circumference comp cone construct the triangle convex surface Corollary cosec decr diagonals diameter distance divided draw equiangular equilateral equivalent feet Find the Log frustum Geom given angle given line given point given side hypothenuse included angle incr inscribed internal angles isosceles triangle lines A B Logarithm M.
M. Sine multiplied number of sides opposite side parallelogram parallelopiped perimeter perpendicular PLANE GEOMETRY plane triangle PLANE TRIGONOMETRY prism PROBLEM quadrilateral radii radius ratio rectangle regular polygon right angle right pyramid right triangle right-angled triangle Scholium secant segment side opposite similar triangles slant height sphere square straight line Tang tangent THEOREM THEOREM VII trapezoid triangle ABC TRIGONOMETRY vertex
Popular passages
Page 30 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 49 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Page 96 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 12 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 71 - The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude.
Page 40 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Page 23 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.