Elements of Plane Geometry According to Euclid |
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Page 7
... 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 is equal to CB ; wherefore CA , AB , BC , are equal to one another ; and the triangle ABC is ...
... 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 is equal to CB ; wherefore CA , AB , BC , are equal to one another ; and the triangle ABC is ...
Page 8
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL ...
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL ...
Page 9
Andrew Bell. equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each ; namely , the ...
Andrew Bell. equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each ; namely , the ...
Page 11
... BC common to both , the two sides DB , BC , are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to ... equal to DB , the angle BDC is equal to the FIRST BOOK . 11.
... BC common to both , the two sides DB , BC , are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to ... equal to DB , the angle BDC is equal to the FIRST BOOK . 11.
Page 12
... equal to AD in the triangle ACD , therefore the angles ECD , FDC , upon the other side of the base CD , are equal to ... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the ...
... equal to AD in the triangle ACD , therefore the angles ECD , FDC , upon the other side of the base CD , are equal to ... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 4 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
Page 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.
Page 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.
Page 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.
Page 27 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Page 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.