The Elements of EuclidDesilver, Thomas, 1838 - 416 sider |
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Side 14
... fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise ...
... fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise ...
Side 18
... fore the 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 ...
... fore the 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 ...
Side 22
... fore the three straight lines KF , FG , GH , are equal to the three A , B , C ; and therefore the triangle KFG has its three sides KF , * See Note . FG , GK equal to three given straight lines , 22 BOOK I THE ELEMENTS OF Euclid .
... fore the three straight lines KF , FG , GH , are equal to the three A , B , C ; and therefore the triangle KFG has its three sides KF , * See Note . FG , GK equal to three given straight lines , 22 BOOK I THE ELEMENTS OF Euclid .
Side 31
... fore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two EA AB are therefore equal to the ...
... fore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two EA AB are therefore equal to the ...
Side 35
... fore the complements , & c . Q. E. D. PROP . XLIV . PROB . To a given straight line to apply a parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . Let AB be the ...
... fore the complements , & c . Q. E. D. PROP . XLIV . PROB . To a given straight line to apply a parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . Let AB be the ...
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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.