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 |
Inni boken
Resultat 1-5 av 98
Side 6
... shown that it cannot have any other position except FE ; and therefore ( ax . 8 ) the angles ABD , EFH are equal . C B G F H This will be illustrated in the remarks on the 28th proposition of the first book ; and the student may ...
... shown that it cannot have any other position except FE ; and therefore ( ax . 8 ) the angles ABD , EFH are equal . C B G F H This will be illustrated in the remarks on the 28th proposition of the first book ; and the student may ...
Side 8
... shown , that BC is equal to BE ; wherefore AF and BC are each of them equal to BE ; and things that are equal to the same are equal ( I. ax . 1 ) to one another ; therefore the straight line AF is equal to BC . Wherefore from the given ...
... shown , that BC is equal to BE ; wherefore AF and BC are each of them equal to BE ; and things that are equal to the same are equal ( I. ax . 1 ) to one another ; therefore the straight line AF is equal to BC . Wherefore from the given ...
Side 10
... shown to coincide with F , in the same manner in which B was shown to coincide with E. Now , B and C coinciding with E and F , the lines between them must coincide so as to exclude space ; for if they did not in every part coincide , a ...
... shown to coincide with F , in the same manner in which B was shown to coincide with E. Now , B and C coinciding with E and F , the lines between them must coincide so as to exclude space ; for if they did not in every part coincide , a ...
Side 12
... shown by taking , first , one side as base , and then another . PROP . VI . THEOR . * If two angles of a triangle be equal to one another , the sides which subtend , or are oppo- site to , those angles , are also equal to one another ...
... shown by taking , first , one side as base , and then another . PROP . VI . THEOR . * If two angles of a triangle be equal to one another , the sides which subtend , or are oppo- site to , those angles , are also equal to one another ...
Side 14
... shown in a similar manner , that the angles FDG , FGD are equal ; and , therefore , ( I. ax . 2 ) the angle EGF , that is , BAC , is equal to EDF . But ( hyp . ) the sides BA , AC are respectively equal to ED , DF , and it has now been ...
... shown in a similar manner , that the angles FDG , FGD are equal ; and , therefore , ( I. ax . 2 ) the angle EGF , that is , BAC , is equal to EDF . But ( hyp . ) the sides BA , AC are respectively equal to ED , DF , and it has now been ...
Andre utgaver - Vis alle
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.