The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthDesilver, Thomas & Company, 1838 - 416 páginas |
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Página 8
... produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight ...
... produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight ...
Página 10
... produce ( 2 . Post . ) the straight lines DA , DB , to E and F ; from the centre B , at the distance BC , describe ( 3. Post . ) the circle CGH , and from the cen- tre D , at the distance DG , describe the circle GKL . AL shall be equal ...
... produce ( 2 . Post . ) the straight lines DA , DB , to E and F ; from the centre B , at the distance BC , describe ( 3. Post . ) the circle CGH , and from the cen- tre D , at the distance DG , describe the circle GKL . AL shall be equal ...
Página 12
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be produced to D and E , the angle ABC shall be equal to ...
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be produced to D and E , the angle ABC shall be equal to ...
Página 14
... produce AC , AD to E , F ; there- 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 ...
... produce AC , AD to E , F ; there- 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 ...
Página 17
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line per- pendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance ...
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line per- pendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance ...
Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference Co-S 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 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 third triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Página 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Página 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Página 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 256 - 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 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Página 20 - ANY two angles of a triangle are together less than two right angles.