The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 13
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base ...
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base ...
Página 15
... join DE , and upon it describe ( 1. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides DA , AF , are ...
... join DE , and upon it describe ( 1. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides DA , AF , are ...
Página 16
... join FC ; the straight line FC drawn from the given point C is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two sides , DC , CF , are equal to the two EC ...
... join FC ; the straight line FC drawn from the given point C is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two sides , DC , CF , are equal to the two EC ...
Página 19
... join BE and produce it to F , and make EF equal to BE ; join also FC , and pro- duce AC to G. B A E F C D Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the an- gle AEB is equal ( 15. 1 ...
... join BE and produce it to F , and make EF equal to BE ; join also FC , and pro- duce AC to G. B A E F C D Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the an- gle AEB is equal ( 15. 1 ...
Página 22
... join KF , KG ; the triangle KFG has its sides equal to the three straight lines A , B , C. K E F G H L ABC Because the point F is in the centre of the circle BKL , FD is equal ( 15. Def . ) to FK ; but FD is equal to the straight line A ...
... join KF , KG ; the triangle KFG has its sides equal to the three straight lines A , B , C. K E F G H L ABC Because the point F is in the centre of the circle BKL , FD is equal ( 15. Def . ) to FK ; but FD is equal to the straight line A ...
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Términos y frases comunes
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 straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 36 - 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.
Página 145 - 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.
Página 65 - 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.
Página 248 - 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.
Página 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 121 - 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 21 - 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.
Página 14 - 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.
Página 80 - 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...
Página 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.