The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 16
... equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; therefore the base AD is equal to ... angles to a given straight line , from a given point in the same . F Let AB be a given straight line , and C a point given ...
... equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; therefore the base AD is equal to ... angles to a given straight line , from a given point in the same . F Let AB be a given straight line , and C a point given ...
Página 17
... angles ; but when a straight line standing on a straight line makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is called a perpendicular to it ; therefore ...
... angles ; but when a straight line standing on a straight line makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is called a perpendicular to it ; therefore ...
Página 18
... angles CBE , EBD are ( 2 Ax . ) equal to the three angles CBA , ABE , EBD . Again , because the angle DBA is equal to the two an- gles DBE , EBA , add to these equals the angle ABC ; therefore the angles DBA , ABC are equal to the three ...
... angles CBE , EBD are ( 2 Ax . ) equal to the three angles CBA , ABE , EBD . Again , because the angle DBA is equal to the two an- gles DBE , EBA , add to these equals the angle ABC ; therefore the angles DBA , ABC are equal to the three ...
Página 19
... equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB . Take away the common angle AED , and the remaining angle CEA is equal ( 3. Ax . ) In the same manner it can be de- to the remaining angle DEB ...
... equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB . Take away the common angle AED , and the remaining angle CEA is equal ( 3. Ax . ) In the same manner it can be de- to the remaining angle DEB ...
Página 24
Euclid Robert Simson. D BAC is equal to the angle A EDG ; therefore the base BC is equal ( 4. 1. ) to the base EG ; and because DG is equal to DF , the angle DFG is equal ( 5. 1. ) to the angle DGF ; but the angle DGF is greater than the ...
Euclid Robert Simson. D BAC is equal to the angle A EDG ; therefore the base BC is equal ( 4. 1. ) to the base EG ; and because DG is equal to DF , the angle DFG is equal ( 5. 1. ) to the angle DGF ; but the angle DGF is greater than the ...
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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.