Elements of geometry and mensuration |
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Page 36
... Shew that only one straight line can be drawn perpendicular to a given straight line from a given point without it . ( 9 ) Shew that the perpendicular is the shortest of all lines from a given point to a given straight line . Of all ...
... Shew that only one straight line can be drawn perpendicular to a given straight line from a given point without it . ( 9 ) Shew that the perpendicular is the shortest of all lines from a given point to a given straight line . Of all ...
Page 37
... Shew that any point in the straight line bi- secting an angle is equidistant from the two straight lines forming the angle . ( 12 ) Shew that any side of a triangle is less than half the sum of all three sides of the same triangle . ( 13 ) ...
... Shew that any point in the straight line bi- secting an angle is equidistant from the two straight lines forming the angle . ( 12 ) Shew that any side of a triangle is less than half the sum of all three sides of the same triangle . ( 13 ) ...
Page 38
... Shew that the straight line drawn from the vertex of the right angle in a right - angled triangle to the middle point of the hypothenuse is equal to half the hypothenuse . Is the ( 25 ) Explain what is meant by the square of a line . of ...
... Shew that the straight line drawn from the vertex of the right angle in a right - angled triangle to the middle point of the hypothenuse is equal to half the hypothenuse . Is the ( 25 ) Explain what is meant by the square of a line . of ...
Page 50
... Shew that the circumferences of circles which have the same centre cannot cut each other . ( 6 ) If the circumference of a circle be divided into four equal arcs , shew that the chords of any two of them , which are adjacent , are at ...
... Shew that the circumferences of circles which have the same centre cannot cut each other . ( 6 ) If the circumference of a circle be divided into four equal arcs , shew that the chords of any two of them , which are adjacent , are at ...
Page 51
... shew that the straight line joining the points of intersection is at right angles to the straight line joining their centres . ( 17 ) Shew that the two tangents , which can be drawn to a circle from a point without it , are equal to one ...
... shew that the straight line joining the points of intersection is at right angles to the straight line joining their centres . ( 17 ) Shew that the two tangents , which can be drawn to a circle from a point without it , are equal to one ...
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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.