The Elements of EuclidDesilver, Thomas, 1838 - 416 sider |
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Side 35
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
Side 38
... reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole an- gle DBA is equal ( 2. Ax . ) to the whole FBC ...
... reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole an- gle DBA is equal ( 2. Ax . ) to the whole FBC ...
Side 42
... reason HF also is a square , and it is upon the side HG , which is equal to AC : therefore HF , CK are the squares of AC , CB ; and because the complement AG is equal ( 43. 1. ) to the complement GE , and that AG is the rectangle ...
... reason HF also is a square , and it is upon the side HG , which is equal to AC : therefore HF , CK are the squares of AC , CB ; and because the complement AG is equal ( 43. 1. ) to the complement GE , and that AG is the rectangle ...
Side 45
... reason , PR is equal to RO ; and because CB is equal to BD , and GK to KN , the rectangle CK is equal ( 36. 1. ) to BN , and GR to RN ; but CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram CO ...
... reason , PR is equal to RO ; and because CB is equal to BD , and GK to KN , the rectangle CK is equal ( 36. 1. ) to BN , and GR to RN ; but CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram CO ...
Side 46
... reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle : and because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) to the interior and opposite ...
... reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle : and because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) to the interior and opposite ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 34 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Side 143 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 63 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 246 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 119 - 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 19 - 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 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Side 78 - 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...
Side 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.