Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult Classes |
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Page 44
... touch the circle , or to be a tangent to the circle , at that point . ] D B Let a straight line AB be drawn at right angles to AC , a diameter of the circle ACD , from the point A one of its extremities ; and let O be the centre of the ...
... touch the circle , or to be a tangent to the circle , at that point . ] D B Let a straight line AB be drawn at right angles to AC , a diameter of the circle ACD , from the point A one of its extremities ; and let O be the centre of the ...
Page 45
... touch- ing the given circle BCD . Find O the centre of the circle ( 50 ) , and join OA ; bisect OA in the point E ; with centre E and radius EA describe the semi - circle AFO meeting the circle BCD in F ; and join AF . AF is B the ...
... touch- ing the given circle BCD . Find O the centre of the circle ( 50 ) , and join OA ; bisect OA in the point E ; with centre E and radius EA describe the semi - circle AFO meeting the circle BCD in F ; and join AF . AF is B the ...
Page 48
... touch each other at one point only ; and the point of contact will be in the straight line which joins the centres , or in that line produced . 1. Let A , and B be the centres of two circles so situated , in the same plane , that AB ...
... touch each other at one point only ; and the point of contact will be in the straight line which joins the centres , or in that line produced . 1. Let A , and B be the centres of two circles so situated , in the same plane , that AB ...
Page 49
... touch each other at that point . In the former case the circles are said to touch each other externally , in the latter internally . 63. PROP . XV . If a straight line touch a circle , and from the point of contact a chord be drawn ...
... touch each other at that point . In the former case the circles are said to touch each other externally , in the latter internally . 63. PROP . XV . If a straight line touch a circle , and from the point of contact a chord be drawn ...
Page 51
... touch a circle at the same point ? ( 20 ) Divide a given arc into four equal parts . ( 21 ) Have equal circles equal circumferences or peri- meters ? Is this the case with equal squares , triangles , and other rectilineal equal plane ...
... touch a circle at the same point ? ( 20 ) Divide a given arc into four equal parts . ( 21 ) Have equal circles equal circumferences or peri- meters ? Is this the case with equal squares , triangles , and other rectilineal equal plane ...
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Common terms and phrases
ABCDEF angular points base bisect centre chain chord circular circumference circumscribed circumscribing circle compasses cone construction cubic curved cylinder describe a circle diagonal diameter distance divided draw a straight drawn edge equal angles equal arcs equilateral triangle feet find the area foot frustum given angle given circle given line given point given ratio given straight line given triangle greater height Hence hexagon inches inscribed instrument intersecting length Let ABCD magnitude measure meet number of sides opposite angle parallelogram parallelopiped perimeter perpendicular plane surface points of division prism PROB produced PROP proportional Protractor radii radius rectangle rectangle contained regular polygon right angles ruler scale segment semi-circle shew shewn similar triangles square of AB square of AC subtends suppose tangent trapezium triangle ABC unit 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 16 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle, shall be greater than the base of the other.
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 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 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 223 - 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 128 - 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.