Elements of Plane Geometry According to EuclidW. and R. Chambers, 1837 - 240 σελίδες |
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Αποτελέσματα 1 - 5 από τα 8.
Σελίδα 45
... gnomon . E D Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is more briefly expressed by the letters AGK , or EHC , which are at the opposite angles of the parallelograms which make the ...
... gnomon . E D Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is more briefly expressed by the letters AGK , or EHC , which are at the opposite angles of the parallelograms which make the ...
Σελίδα 48
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD DB . To each of these add LG , which is equal to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD DB , together with the ...
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD DB . To each of these add LG , which is equal to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD DB , together with the ...
Σελίδα 49
... gnomon CMG . Now , AM is the rectangle contained by AD , DB , for DM is equal to DB ( II . 4 , Cor . ) ; there- fore the gnomon CMG is equal to the rectangle ADDB ; add to each of these LG , which is equal to the square of CB ...
... gnomon CMG . Now , AM is the rectangle contained by AD , DB , for DM is equal to DB ( II . 4 , Cor . ) ; there- fore the gnomon CMG is equal to the rectangle ADDB ; add to each of these LG , which is equal to the square of CB ...
Σελίδα 50
... gnomon AKF , together with the square CK ; therefore the gnomon AKF , together with the square CK , is double of AK . But twice the rectangle ABBC is also double of AK , for BK is equal to BC ( II . 4 , Cor . ) ; therefore the gnomon ...
... gnomon AKF , together with the square CK ; therefore the gnomon AKF , together with the square CK , is double of AK . But twice the rectangle ABBC is also double of AK , for BK is equal to BC ( II . 4 , Cor . ) ; therefore the gnomon ...
Σελίδα 51
... gnomon AOH , are quadruple of AK . And because AK is the rectangle contained by AB , BC , for BK is equal to BC , four times the rectangle AB BC is quadruple of AK . But the gnomon AOH was demon- strated to be quadruple of AK ...
... gnomon AOH , are quadruple of AK . And because AK is the rectangle contained by AB , BC , for BK is equal to BC , four times the rectangle AB BC is quadruple of AK . But the gnomon AOH was demon- strated to be quadruple of AK ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry, According to Euclid: As Improved by Simson and ... Andrew Bell,Associate Professor of History Andrew Bell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2008 |
Elements of Plane Geometry, According to Euclid: As Improved by Simson and ... Andrew Bell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2008 |
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 number of sides opposite angle parallel parallelogram perimeter perpendicular polygon porism produced proportional PROPOSITION radius 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.