Elements of geometry and mensuration |
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Page 11
... square and a triangle , and we can cut up the square , so as with the parts exactly to cover the triangle , the area of the square is equal to that of the triangle . Or , again , two triangles , which to the eye appear unequal , may yet ...
... square and a triangle , and we can cut up the square , so as with the parts exactly to cover the triangle , the area of the square is equal to that of the triangle . Or , again , two triangles , which to the eye appear unequal , may yet ...
Page 30
... square . For AB AD ; = and ABED is a parallelogram , which has its opposite sides equal , and also its A opposite ... square , and it is described upon the line AB . COR . 1. If the side of one square be equal to the side of another ...
... square . For AB AD ; = and ABED is a parallelogram , which has its opposite sides equal , and also its A opposite ... square , and it is described upon the line AB . COR . 1. If the side of one square be equal to the side of another ...
Page 32
... square on BC + the square on AC - the parallelogram BILE + the parallelogram AILD = the square ABED = square on AB . N. B. The square described upon a line is generally called , for shortness , the square of that line . Thus the square ...
... square on BC + the square on AC - the parallelogram BILE + the parallelogram AILD = the square ABED = square on AB . N. B. The square described upon a line is generally called , for shortness , the square of that line . Thus the square ...
Page 33
... square ADEB ( 42 ) ; join BD ; through the point C draw CGF parallel to AD or BE , and meeting BDin G ; and through ... square ; and it is the square of BC . Similarly it may be shewn , that HGFD is a square ; and it is the square of HG ...
... square ADEB ( 42 ) ; join BD ; through the point C draw CGF parallel to AD or BE , and meeting BDin G ; and through ... square ; and it is the square of BC . Similarly it may be shewn , that HGFD is a square ; and it is the square of HG ...
Page 34
... square BCGK , and then the rectangle ABKH = the rectangle EBCF ; .. ABKH + EBCF twice the rectangle ABKH = twice the rect- angle contained by AB , BC . Now add to these equals the square HDFG , which is the square of AC ; then ABKH + ...
... square BCGK , and then the rectangle ABKH = the rectangle EBCF ; .. ABKH + EBCF twice the rectangle ABKH = twice the rect- angle contained by AB , BC . Now add to these equals the square HDFG , which is the square of AC ; then ABKH + ...
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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.