Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult ClassesLongman, 1859 - 362 páginas |
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Página 15
... Suppose them unequal , and proceeding upon this assumption we arrive , by means of acknow- ledged axioms and legitimate reasoning , at an absurd conclusion , such as , for instance , that a portion of a mag- nitude is greater than the ...
... Suppose them unequal , and proceeding upon this assumption we arrive , by means of acknow- ledged axioms and legitimate reasoning , at an absurd conclusion , such as , for instance , that a portion of a mag- nitude is greater than the ...
Página 17
... Suppose the = LEDF . triangle ABC to be laid upon the triangle DEF , in such manner that the point A is upon the point D , and the line AB upon DE ; then the point B will fall AA B upon E , because AB = DE . Again , since AB falls upon ...
... Suppose the = LEDF . triangle ABC to be laid upon the triangle DEF , in such manner that the point A is upon the point D , and the line AB upon DE ; then the point B will fall AA B upon E , because AB = DE . Again , since AB falls upon ...
Página 45
... suppose OAB not a right angle . From O draw OE at right angles to AB , meeting the circumference in F ; then OAE is a triangle , of which OEA is a right angle , and .. < OAE less than a right angle ; .. the side OA is greater than the ...
... suppose OAB not a right angle . From O draw OE at right angles to AB , meeting the circumference in F ; then OAE is a triangle , of which OEA is a right angle , and .. < OAE less than a right angle ; .. the side OA is greater than the ...
Página 46
... suppose the one circle to be laid upon the other , so that the centre E shall be upon F ; then since the radii are equal , the whole circumference of one will coincide with the whole circumference of the other ; and , without altering ...
... suppose the one circle to be laid upon the other , so that the centre E shall be upon F ; then since the radii are equal , the whole circumference of one will coincide with the whole circumference of the other ; and , without altering ...
Página 55
... suppose , as the e process is the same whatever the number may be . D E From A draw any other indefinite line Ab , forming an angle with AB ; in Ab take any point D conveni- ently near to A , and with centre D and radius DA describe a ...
... suppose , as the e process is the same whatever the number may be . D E From A draw any other indefinite line Ab , forming an angle with AB ; in Ab take any point D conveni- ently near to A , and with centre D and radius DA describe a ...
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Términos y frases comunes
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 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
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 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.
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 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 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 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.
Página 128 - 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.