Elements of geometry and mensurationLongman, Brown, Green, and Longmans, 1854 - 192 páginas |
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Página 10
... construction and treatment of Geometrical figures . In ' describing ' a circle , by the third Postulate , we trace out the circumference which is the boundary of the circle . Of course we can trace a part , as well as the whole , that ...
... construction and treatment of Geometrical figures . In ' describing ' a circle , by the third Postulate , we trace out the circumference which is the boundary of the circle . Of course we can trace a part , as well as the whole , that ...
Página 22
... construction , and 2 AEB = = △ CEF ( 31 ) , because they are opposite vertical angles , the triangles AEB , CEF are equal in all re- spects ( 24 ) , and the angles are equal to which the equal sides are opposite , so that BAE = ECF ...
... construction , and 2 AEB = = △ CEF ( 31 ) , because they are opposite vertical angles , the triangles AEB , CEF are equal in all re- spects ( 24 ) , and the angles are equal to which the equal sides are opposite , so that BAE = ECF ...
Página 33
... construction , its opposite sides are equal to each other , and likewise its op- posite angles ( 40 ) , that is , BC = D F E KG , BK = CG , △ CBK = CGK , and BCG = BKG . But since BE - ED , .. ‹ EBD = ¿ EDB ( 26 ) ; and since KG is ...
... construction , its opposite sides are equal to each other , and likewise its op- posite angles ( 40 ) , that is , BC = D F E KG , BK = CG , △ CBK = CGK , and BCG = BKG . But since BE - ED , .. ‹ EBD = ¿ EDB ( 26 ) ; and since KG is ...
Página 34
... construction as in ( 44 ) , and in the same manner it may be shewn , that BCGK , and HGFD , are the squares of BC , and AC ; and that ACGH is a rectangle , and EFGK , which is also a rectangle . Add to each of these equals the square ...
... construction as in ( 44 ) , and in the same manner it may be shewn , that BCGK , and HGFD , are the squares of BC , and AC ; and that ACGH is a rectangle , and EFGK , which is also a rectangle . Add to each of these equals the square ...
Página 36
... construction , what figure will the two together make ? ( 2 ) Have we yet laid down any mode of measuring an angle ? If not , how are we able to prove that one angle is equal to , less than , or greater than , another ac- cording to ...
... construction , what figure will the two together make ? ( 2 ) Have we yet laid down any mode of measuring an angle ? If not , how are we able to prove that one angle is equal to , less than , or greater than , another ac- cording to ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 19 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 126 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Página 20 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.