Elements of geometry: consisting of the first four,and the sixth, books of Euclid, with the principal theorems in proportion [&c.] by J. Narrien1842 |
Inni boken
Resultat 1-5 av 57
Side
... diameters , does not state expressly that the sides of the inscribed polygons are less than the least assignable lines , but that the series of inscribed polygons is continued till there is obtained , in one of the circles , a polygon ...
... diameters , does not state expressly that the sides of the inscribed polygons are less than the least assignable lines , but that the series of inscribed polygons is continued till there is obtained , in one of the circles , a polygon ...
Side 3
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . A semidiameter of a circle is now usually called the radius . XVIII . A semicircle is the figure contained by a diameter ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . A semidiameter of a circle is now usually called the radius . XVIII . A semicircle is the figure contained by a diameter ...
Side 31
... diameter , or diagonal , is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC ...
... diameter , or diagonal , is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC ...
Side 32
... diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC is equal to the angle BCD ; therefore the triangle ABC is equal ( 4.1 . ) to the triangle ...
... diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC is equal to the angle BCD ; therefore the triangle ABC is equal ( 4.1 . ) to the triangle ...
Side 34
... diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are equal ( 7. Ax . ) ; therefore the triangle ABC is equivalent to the ...
... diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are equal ( 7. Ax . ) ; therefore the triangle ABC is equivalent to the ...
Andre utgaver - Vis alle
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2013 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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
Side 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.
Side 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.
Side 9 - If two triangles have two sides of the one equal to two sides of the...