Elements of geometry: consisting of the first four,and the sixth, books of Euclid, with the principal theorems in proportion [&c.] by J. Narrien1842 |
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... found from the cylinders formed by the revolution of rect- angles inscribed within , and described about the circle ... rectangle AD . DE , which , being contained by lines not less than the least that can be assigned , is not less than ...
... found from the cylinders formed by the revolution of rect- angles inscribed within , and described about the circle ... rectangle AD . DE , which , being contained by lines not less than the least that can be assigned , is not less than ...
Página 44
... rectangle contained by the two straight lines , is equal to the rectangles con- tained by the undivided line , and ... rectangle contained by the straight lines A , BC is equal to the rectangle contained G B D E C F K H A by ELEMENTS ...
... rectangle contained by the two straight lines , is equal to the rectangles con- tained by the undivided line , and ... rectangle contained by the straight lines A , BC is equal to the rectangle contained G B D E C F K H A by ELEMENTS ...
Página 45
... contained by A , EC . From the point в draw ( 11. 1. ) BF at right angles to BC , and make BG equal ( 3.1 . ) to A ... rectangle BH is equal to the rectangles BK , DL , EH : but BH is contained by A , BC , for it is contained by GB , BC ...
... contained by A , EC . From the point в draw ( 11. 1. ) BF at right angles to BC , and make BG equal ( 3.1 . ) to A ... rectangle BH is equal to the rectangles BK , DL , EH : but BH is contained by A , BC , for it is contained by GB , BC ...
Página 46
... rectangle A E is equal to the rectangles AD , CE ; and AE is the rectangle contained by AB , BC , for it is contained by AB , BE , of which BE is equal to BC ; and AD is contained by AC , CB , for CD is equal to CB ; and DB is the ...
... rectangle A E is equal to the rectangles AD , CE ; and AE is the rectangle contained by AB , BC , for it is contained by AB , BE , of which BE is equal to BC ; and AD is contained by AC , CB , for CD is equal to CB ; and DB is the ...
Página 47
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : and HF , CK are the squares of AC , CB ; wherefore the four ...
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : and HF , CK are the squares of AC , CB ; wherefore the four ...
Otras ediciones - Ver todas
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Sin vista previa disponible - 2015 |
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Sin vista previa disponible - 2018 |
Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides Sin vista previa disponible - 2013 |
Términos y frases comunes
ABCD AC is equal adjacent angles altitudes angle ABC angle ACB angle BAC assigned base BC bisected centre circle ABC circumference cone convex surface cylinder described diameter draw drawn duplicate ratio Edition equal angles equal or equivalent equi equilateral and equiangular Euclid exterior angle fore given line given rectilineal given straight line gnomon greater Greek homologous homologous sides inscribed join Latin Let ABC measure number of sides opposite angles parallel parallelepiped parallelogram perpendicular picket plane angles prism PROB proportional proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure regular polygon remaining angle right angles segment similar solid angle sphere spherical angle square of AC straight line AC THEOR touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 55 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Página 47 - CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line, &c.
Página 12 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Página 73 - CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED.
Página 8 - A New Treatise on the Use of the Globes ; or, a Philosophical View of the Earth and Heavens : comprehending an Account of the Figure, Magnitude, and Motion of the Earth: with the Natural Changes of its Surface, caused by Floods, Earthquakes, &c.
Página 142 - 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.
Página 11 - ABC is therefore equal to the remaining angle ACB, which are the angles at the base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore, " the angles at the base
Página 53 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Página 30 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Página 9 - If two triangles have two sides of the one equal to two sides of the...