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 Seiten |
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Seite 10
... equal ( 15. Definition . ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal ...
... equal ( 15. Definition . ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal ...
Seite 11
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB .. FROM the greater ...
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB .. FROM the greater ...
Seite 12
... equal to it . Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them , viz , the ...
... equal to it . Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them , viz , the ...
Seite 13
... 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 whole ACF , the parts of 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 whole ACF , the parts of which , the ...
Seite 14
... equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : but the angle ACD is greater than the angle BCD ; therefore the angle ADC is great- er also than BCD ; much more then is the angle BDC greater than the angle BCD . Again ...
... equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : but the angle ACD is greater than the angle BCD ; therefore the angle ADC is great- er also than BCD ; much more then is the angle BDC greater than the angle BCD . Again ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Seite 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.
Seite 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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...
Seite 20 - ANY two angles of a triangle are together less than two right angles.