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, and G. G. & J. Robinson, London., 1795 - 400 σελίδες |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 57
... sum , and AC the dif- " ference of the lines AB and BC , four times the rectangle " contained by any two lines together with the square of their difference , is equal to the square of the sum of the 66 " lines . " " COR . 2. From the ...
... sum , and AC the dif- " ference of the lines AB and BC , four times the rectangle " contained by any two lines together with the square of their difference , is equal to the square of the sum of the 66 " lines . " " COR . 2. From the ...
Σελίδα 66
... sum of the squares of AC and BD is equal to the sum of the squares of AB , BC , CD , DA . Let AC and BD interfect one another in E : and because the vertical angles AED , CEB are equal a , and also the al- ternate angles EAD , ECB b ...
... sum of the squares of AC and BD is equal to the sum of the squares of AB , BC , CD , DA . Let AC and BD interfect one another in E : and because the vertical angles AED , CEB are equal a , and also the al- ternate angles EAD , ECB b ...
Σελίδα 134
... sum of those mag- nitudes or numbers . Thus , A + B is the sum of the two magnitudes denoted by the letters A and B ; m + n is the fum of the numbers denoted by m and n . 3. The fign - ( minus ) , written between two letters fig- nifies ...
... sum of those mag- nitudes or numbers . Thus , A + B is the sum of the two magnitudes denoted by the letters A and B ; m + n is the fum of the numbers denoted by m and n . 3. The fign - ( minus ) , written between two letters fig- nifies ...
Σελίδα 136
... sum of all the reft . 1 Let any number of magnitudes A , B , and C be equimul- tiples of as many others D , E , and ... sum will be the same multiple of that magnitude that the sum of the two numbers is of unity . Let AmC , and B ...
... sum of all the reft . 1 Let any number of magnitudes A , B , and C be equimul- tiples of as many others D , E , and ... sum will be the same multiple of that magnitude that the sum of the two numbers is of unity . Let AmC , and B ...
Σελίδα 243
... sum of the prisms shall exceed the pyramid by a folid less than any given solid . Let ABCD be a pyramid , and Z + a given solid ; a series of prisms having all the fame altitude , may be circumscribed about the pyramid ABCD , so that ...
... sum of the prisms shall exceed the pyramid by a folid less than any given solid . Let ABCD be a pyramid , and Z + a given solid ; a series of prisms having all the fame altitude , may be circumscribed about the pyramid ABCD , so that ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD alfo alſo 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 drawn equal angles equiangular 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 perpendicular plane polygon priſm proportionals propoſition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſame ſame baſe ſame manner ſame ratio ſecond ſection ſegment ſemicircle ſhall 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
Δημοφιλή αποσπάσματα
Σελίδα 27 - 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...
Σελίδα 165 - 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.
Σελίδα 18 - 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.
Σελίδα 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.
Σελίδα 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.
Σελίδα 33 - 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.
Σελίδα 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.
Σελίδα 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 166 - 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...
Σελίδα 54 - 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...