Elements of Plane Geometry According to EuclidW. and R. Chambers, 1837 - 240 páginas |
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Página 7
... AC is equal ( Definition 14 ) 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 ; therefore ( Axiom 1 ) CA ...
... AC is equal ( Definition 14 ) 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 ; therefore ( Axiom 1 ) CA ...
Página 8
... equal to the remainder BG ( Ax . 3 ) : But it has been shown that BC is equal to BG ; wherefore AL and BC are each ... AC , equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF ; and the angle BAC equal to the ...
... equal to the remainder BG ( Ax . 3 ) : But it has been shown that BC is equal to BG ; wherefore AL and BC are each ... AC , equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF ; and the angle BAC equal to the ...
Página 9
... equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : but the point B coincides ...
... equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : but the point B coincides ...
Página 10
... equal sides are op- posite ; namely , the angle ACF to the angle ABG , and the angle AFC to the angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC , the remainder BF shall be equal ( Ax . 3 ) ...
... equal sides are op- posite ; namely , the angle ACF to the angle ABG , and the angle AFC to the angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC , the remainder BF shall be equal ( Ax . 3 ) ...
Página 11
... equal to one another . D Let ABC be a triangle having the angle ABC equal to the angle ACB , the side AB is also equal to the side AC . For , if AB be not equal to AC , one of them is greater than the other : Let AB be the greater , and ...
... equal to one another . D Let ABC be a triangle having the angle ABC equal to the angle ACB , the side AB is also equal to the side AC . For , if AB be not equal to AC , one of them is greater than the other : Let AB be the greater , and ...
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Elements of Plane Geometry According to Euclid Robert Simson,Formerly Chairman Department of Immunology John Playfair,John Playfair Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD AC is equal angle ABC angle ACB angle BAC angle BCD angle EDF apothem base BC bisected centre chord circle ABC circumference described diameter double draw equal angles equal to AC equiangular equilateral polygon equimultiples exterior angle fore geometry given circle given line given point given rectilineal given straight line gnomon greater hypotenuse inscribed interminate less Let ABC magnitudes multiple opposite angle parallel parallelogram perimeter perpendicular polygon porism produced proportional PROPOSITION radius rectangle AB BC rectangle contained rectilineal figure regular polygon remaining angle right angles right-angled triangle Schol segment semicircle semiperimeter similar sine square of AC tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vulgar fraction wherefore
Pasajes populares
Página 1 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another.
Página 73 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 9 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Página 4 - If two triangles have two sides of the one equal to two sides of the...
Página 139 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (2.
Página 23 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
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 80 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. 7. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.
Página 27 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Página 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.