Elements of Geometry: Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical TrigonometryBell & Bradfute, 1795 - 400 Seiten |
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Seite 66
... interfect one another in E : and because the vertical angles AED , CEB are equal a , and also the al- ternate angles EAD , ECB b , the triangles ADE , CEB have two angles in the one equal to two angles in the other , each to each : but ...
... interfect one another in E : and because the vertical angles AED , CEB are equal a , and also the al- ternate angles EAD , ECB b , the triangles ADE , CEB have two angles in the one equal to two angles in the other , each to each : but ...
Seite 312
... interfect one another in A , and let BC be an arch of another great circle , of which the pole is A ; BC is the measure of the spherical angle BAС . Join AD , DB , DC ; fince A is the pole of BC , AB , AC are quadrants , and the angles ...
... interfect one another in A , and let BC be an arch of another great circle , of which the pole is A ; BC is the measure of the spherical angle BAС . Join AD , DB , DC ; fince A is the pole of BC , AB , AC are quadrants , and the angles ...
Seite 319
... interfect each other . In the same manner , D is the pole of BC , and E the pole of AB . K D N M B C A G T E H And fince F , E are the poles of AL , AM , the arches FL and EM are quadrants , and FL , EM together , that is , FE and ML ...
... interfect each other . In the same manner , D is the pole of BC , and E the pole of AB . K D N M B C A G T E H And fince F , E are the poles of AL , AM , the arches FL and EM are quadrants , and FL , EM together , that is , FE and ML ...
Seite 351
... interfect one another in two points , and yet in the intermediate part must not coincide , and there- fore by the definition they are not straight lines . It follows in the same way , that two straight lines cannot have a com- mon ...
... interfect one another in two points , and yet in the intermediate part must not coincide , and there- fore by the definition they are not straight lines . It follows in the same way , that two straight lines cannot have a com- mon ...
Seite 360
... interfect one ano- ther . PROP . XXIV . The subject of parallel lines is one of the most difficult in the Elements of Geometry . It has accordingly been treated of in a great variety of different ways , of which , perhaps , there is ...
... interfect one ano- ther . PROP . XXIV . The subject of parallel lines is one of the most difficult in the Elements of Geometry . It has accordingly been treated of in a great variety of different ways , of which , perhaps , there is ...
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ABCD alfo alſo alſo equal angle ABC angle ACB angle BAC arch baſe baſe BC BC is equal becauſe becauſe the angle biſected Book VII caſe cauſe centre circle ABC circumference co-fine demonſtrated deſcribed diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fame reaſon fides fimilar fince firſt folid fore given ſtraight line greater inſcribed interfect join leſs Let ABC line BC magnitudes oppoſite parallel parallelepiped parallelogram paſs paſſes perpendicular plane polygon priſm proportionals propoſition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſame ſame manner ſame ratio ſecond ſection ſegment ſhall be equal ſhewn ſide ſolid ſpace ſpherical triangle ſquare of AC ſtand ſuch ſum ſuppoſed tangent THEOR theſe thoſe touches the circle triangle ABC wherefore
Beliebte Passagen
Seite 19 - 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. either the sides adjacent to the equal...
Seite 155 - 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.
Seite 17 - 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.
Seite 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.
Seite 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 23 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 12 - 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, &c.
Seite 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 156 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...
Seite 44 - 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...