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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 93.
Σελίδα 5
... meet together , but are not in the same direc- tion . " IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . A D B C E * See Notes . 6 ...
... meet together , but are not in the same direc- tion . " IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . A D B C E * See Notes . 6 ...
Σελίδα 6
... meet one another , is put between the other ' two letters , and one of these two is somewhere upon one of those straight lines , and the other upon the other line : Thus the angle ' which is contained by the straight lines AB , CB , is ...
... meet one another , is put between the other ' two letters , and one of these two is somewhere upon one of those straight lines , and the other upon the other line : Thus the angle ' which is contained by the straight lines AB , CB , is ...
Σελίδα 8
... 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 line . III . And that a circle may be ...
... 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 line . III . And that a circle may be ...
Σελίδα 9
... meet two straight lines , so as to make the two " interior angles on the same side of it taken together less than " two right angles , these straight lines being continually pro- " duced , shall at length meet upon that side on which ...
... meet two straight lines , so as to make the two " interior angles on the same side of it taken together less than " two right angles , these straight lines being continually pro- " duced , shall at length meet upon that side on which ...
Σελίδα 26
... meet towards B , D. In like manner it may be demonstrat- C ed that they do not meet to- F wards A , C ; but those straight B G D lines which meet neither way , though produced ever so far , are parallel ( 35. def . ) to one another . AB ...
... meet towards B , D. In like manner it may be demonstrat- C ed that they do not meet to- F wards A , C ; but those straight B G D lines which meet neither way , though produced ever so far , are parallel ( 35. def . ) to one another . AB ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Σελίδα 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.
Σελίδα 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 20 - ANY two angles of a triangle are together less than two right angles.