Elements of Plane Geometry According to EuclidW. and R. Chambers, 1837 - 240 σελίδες |
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Αποτελέσματα 1 - 5 από τα 32.
Σελίδα 31
... ABCD shall be equal to the parallelogram EBCF . D If the sides AD , DF , of the parallelograms ABCD , DBCF , opposite to the base BC , be termi- nated in the same point D , it is plain that each of the parallelograms is double of the ...
... ABCD shall be equal to the parallelogram EBCF . D If the sides AD , DF , of the parallelograms ABCD , DBCF , opposite to the base BC , be termi- nated in the same point D , it is plain that each of the parallelograms is double of the ...
Σελίδα 32
... ABCD is equal to the parallelogram EBCF . PROPOSITION XXXVI . THEOREM . Parallelograms upon equal bases , and between the same parallels , are equal to one another . Let ABCD , EFGH , be parallelograms upon equal bases BC , FG , and ...
... ABCD is equal to the parallelogram EBCF . PROPOSITION XXXVI . THEOREM . Parallelograms upon equal bases , and between the same parallels , are equal to one another . Let ABCD , EFGH , be parallelograms upon equal bases BC , FG , and ...
Σελίδα 35
... ABCD and the triangle EBC be the same base BC , and between the same parallels BC , upon AE , the parallelogram ABCD is double of the triangle FIRST BOOK . 35.
... ABCD and the triangle EBC be the same base BC , and between the same parallels BC , upon AE , the parallelogram ABCD is double of the triangle FIRST BOOK . 35.
Σελίδα 36
... ABCD is double of the triangle ABC ( I. 34 ) , because the diameter AC divides it into two equal parts ; wherefore ABCD is also double of the triangle EBC . PROPOSITION XLII . PROBLEM . To describe a parallelogram that shall be equal to ...
... ABCD is double of the triangle ABC ( I. 34 ) , because the diameter AC divides it into two equal parts ; wherefore ABCD is also double of the triangle EBC . PROPOSITION XLII . PROBLEM . To describe a parallelogram that shall be equal to ...
Σελίδα 37
... ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . Because ABCD is a parallelogram , and AC its diagonal , the triangle ABC is equal to the triangle ADC ( Ï.34 ) . And because EKHA is a ...
... ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . Because ABCD is a parallelogram , and AC its diagonal , the triangle ABC is equal to the triangle ADC ( Ï.34 ) . And because EKHA is a ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry According to Euclid Robert Simson,Formerly Chairman Department of Immunology John Playfair,John Playfair Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 27 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 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.