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
... gles . XXXIV . All other four sided figures besides these , are called trapeziums . XXXV . Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET ...
... gles . XXXIV . All other four sided figures besides these , are called trapeziums . XXXV . Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET ...
Página 12
... BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal ( 4. 1. ) and their remaining an- E gles , each to each , to which the equal 12 BOOK I. THE ELEMENTS OF EUCLID .
... BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal ( 4. 1. ) and their remaining an- E gles , each to each , to which the equal 12 BOOK I. THE ELEMENTS OF EUCLID .
Página 13
... gles , each to each , to which the equal sides , are 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 ...
... gles , each to each , to which the equal sides , are 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 ...
Página 15
... gles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC ...
... gles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC ...
Página 17
... gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal ( 15 Def . 1. ) to the base CG ; therefore the angle CHF is equal ( 8. 1. ) to the angle CHG ; and they are adjacent angles ...
... gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equal ( 15 Def . 1. ) to the base CG ; therefore the angle CHF is equal ( 8. 1. ) to the angle CHG ; and they are adjacent angles ...
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.