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
... opposite sides equal to one another , but all its sides are not equal , nor its angles right an- gles . XXXIV . All other four sided figures besides these , are called trapeziums . XXXV . Parallel straight lines , are such as are in the ...
... opposite sides equal to one another , but all its sides are not equal , nor its angles right an- gles . XXXIV . All other four sided figures besides these , are called trapeziums . XXXV . Parallel straight lines , are such as are in the ...
Página 11
... opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF , the base BC shall be equal to the base ...
... opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF , the base BC shall be equal to the base ...
Página 12
... opposite shall be equal , each to each . Which was to be demonstrated . PROP . V. THEOR . THE angles at the base of an isosceles triangle are equal to one another : and , if the equal sides be produced , the angles upon the other side ...
... opposite shall be equal , each to each . Which was to be demonstrated . PROP . V. THEOR . THE angles at the base of an isosceles triangle are equal to one another : and , if the equal sides be produced , the angles upon the other side ...
Página 13
... opposite ; there- fore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG ; and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF ...
... opposite ; there- fore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG ; and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF ...
Página 18
... opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD upon ...
... opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD upon ...
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.