Elements of geometry and mensuration |
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Page 16
... given straight line ↑ . Let AB be the given straight line , which is to be one side of the triangle ; with centre A and radius AB ( POST . III . 20 ) trace a portion of the circumference of a circle on that side of AB on which the ...
... given straight line ↑ . Let AB be the given straight line , which is to be one side of the triangle ; with centre A and radius AB ( POST . III . 20 ) trace a portion of the circumference of a circle on that side of AB on which the ...
Page 19
... given straight line * from a given point in it . Let AB be the given straight line , and C a given point in it . It is re- quired to draw a straight line from C at right angles to AB . In AC take any point D , and with centre C , and ...
... given straight line * from a given point in it . Let AB be the given straight line , and C a given point in it . It is re- quired to draw a straight line from C at right angles to AB . In AC take any point D , and with centre C , and ...
Page 36
... given straight line , how much is taken for granted ? If a second triangle be drawn on the opposite side of the line by a similar construction , what figure will the two together make ? ( 2 ) Have we yet laid down any mode of measuring ...
... given straight line , how much is taken for granted ? If a second triangle be drawn on the opposite side of the line by a similar construction , what figure will the two together make ? ( 2 ) Have we yet laid down any mode of measuring ...
Page 38
... given line . ( 29 ) Is the rectangle contained by AB , BC , the same as that contained by CB , BA ? or that contained by BC , AB ? ( 30 ) Make a rectangle which shall be double of a given rectangle AB , BC . ( 31 ) Is it certain à ...
... given line . ( 29 ) Is the rectangle contained by AB , BC , the same as that contained by CB , BA ? or that contained by BC , AB ? ( 30 ) Make a rectangle which shall be double of a given rectangle AB , BC . ( 31 ) Is it certain à ...
Page 41
... given points . Let A , B , C , be the three given points ; join AB , and BC . Bisect AB in D , and BC in E ; from D draw DF at right angles to AB ; and from E draw EG at right angles to BC , intersecting DF in 0 ; with centre ✪ and ra ...
... given points . Let A , B , C , be the three given points ; join AB , and BC . Bisect AB in D , and BC in E ; from D draw DF at right angles to AB ; and from E draw EG at right angles to BC , intersecting DF in 0 ; with centre ✪ and ra ...
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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.