The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and IllustrationsLongmans, Green, 1845 - 352 sider |
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Side xii
... greater than a right angle . 10. An acute angle is that which is less than a right angle . 11. Parallel straight lines are those which are in the same plane , and which , being produced ever so far both ways , do not meet . 12. A figure ...
... greater than a right angle . 10. An acute angle is that which is less than a right angle . 11. Parallel straight lines are those which are in the same plane , and which , being produced ever so far both ways , do not meet . 12. A figure ...
Side 2
... greater than a right angle . 10. An acute angle is that which is less than a right angle . 11. Parallel straight lines are those which are in the same plane , and which , being produced ever so far both ways , do not meet . 12. A figure ...
... greater than a right angle . 10. An acute angle is that which is less than a right angle . 11. Parallel straight lines are those which are in the same plane , and which , being produced ever so far both ways , do not meet . 12. A figure ...
Side 6
... greater , or taking from it , is greater than that which is obtained by adding to the less , or taking from it . † This axiom might be derived from axiom 2 ; and the next from this one by an indirect demonstration . They are generalized ...
... greater , or taking from it , is greater than that which is obtained by adding to the less , or taking from it . † This axiom might be derived from axiom 2 ; and the next from this one by an indirect demonstration . They are generalized ...
Side 9
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( I. 2 ) the straight line AD equal to C ; and from the centre A , at the distance AD , describe ( I. post . 3 ) the circle ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( I. 2 ) the straight line AD equal to C ; and from the centre A , at the distance AD , describe ( I. post . 3 ) the circle ...
Side 10
... greater than DE . Again , the angles A and D are equal ; that is , the opening of the lines AB , AC is equal to that of DE and DF . Hence , AB coincid- ing with DE , AC must coincide with DF . For if AC fell beyond DF , the angle A ...
... greater than DE . Again , the angles A and D are equal ; that is , the opening of the lines AB , AC is equal to that of DE and DF . Hence , AB coincid- ing with DE , AC must coincide with DF . For if AC fell beyond DF , the angle A ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained corollary cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB.-To produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar solid angles square of AC straight line drawn tangent THEOR.-If third triangle ABC trigonometry triplicate ratio vertex vertical angle wherefore
Populære avsnitt
Side 130 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 45 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Side 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Side 50 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Side 38 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 7 - If two triangles have two sides of the one equal to two sides of the...
Side 27 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 27 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 36 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.