The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 12
... common to the two triangles AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other ...
... common to the two triangles AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other ...
Página 13
... 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 DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1 ...
... 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 DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1 ...
Página 15
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides , EA , AF each to each ; and the base DF is equal to the base EF ; therefore the angle DAF is equal ( 8. 1. ) to the angle EAF ; wherefore the ...
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides , EA , AF each to each ; and the base DF is equal to the base EF ; therefore the angle DAF is equal ( 8. 1. ) to the angle EAF ; wherefore the ...
Página 16
... common segment . If it be possible , let the two straight lines ABC , ABD have the seg- ment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC is a straight line , the angle CBE is equal ( 10 ...
... common segment . If it be possible , let the two straight lines ABC , ABD have the seg- ment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC is a straight line , the angle CBE is equal ( 10 ...
Página 17
... common to the two trian- gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal ( 15 Def . 1. ) to the base CG ; therefore the angle CHF is equal ( 8. 1. ) to the angle CHG ; and ...
... common to the two trian- gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal ( 15 Def . 1. ) to the base CG ; therefore the angle CHF is equal ( 8. 1. ) to the angle CHG ; and ...
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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 square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 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.
Página 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.
Página 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.
Página 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...
Página 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.