Elements of Plane Geometry According to EuclidW. and R. Chambers, 1837 - 240 σελίδες |
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Αποτελέσματα 1 - 5 από τα 30.
Σελίδα 7
... BCD , and from the centre B , at the dis- tance BA , describe the circle ACE ; and from the point C , in which the ... angle DAB , and produce ( Post . 2 ) the straight lines DA , DB , to E and F ; from the centre B , with the ...
... BCD , and from the centre B , at the dis- tance BA , describe the circle ACE ; and from the point C , in which the ... angle DAB , and produce ( Post . 2 ) the straight lines DA , DB , to E and F ; from the centre B , with the ...
Σελίδα 11
... 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 ... BCD ; therefore the angle ADC is greater also than BCD ; still greater , then , is the angle BDC than the angle ...
... 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 ... BCD ; therefore the angle ADC is greater also than BCD ; still greater , then , is the angle BDC than the angle ...
Σελίδα 12
... BCD ; but it has been demonstrated to be greater than it ; which is im- possible . But if one of the vertices , as D , be within the other tri- angle ... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise ...
... BCD ; but it has been demonstrated to be greater than it ; which is im- possible . But if one of the vertices , as D , be within the other tri- angle ... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise ...
Σελίδα 13
... angle BAC coincides with the angle EDF , and is equal ( Ax . 8 ) to it . PROPOSITION IX . PROBLEM . To bisect a ... BCD ; the two sides AC , CD , are equal to the FIRST BOOK . 13.
... angle BAC coincides with the angle EDF , and is equal ( Ax . 8 ) to it . PROPOSITION IX . PROBLEM . To bisect a ... BCD ; the two sides AC , CD , are equal to the FIRST BOOK . 13.
Σελίδα 14
... angle ACD is also equal to the angle BCD ; therefore the base AD is equal to the base DB ( 1.4 ) , and the straight line AB is divided into two equal parts in the point D. PROPOSITION XI . PROBLEM . To draw a straight line at right angles ...
... angle ACD is also equal to the angle BCD ; therefore the base AD is equal to the base DB ( 1.4 ) , and the straight line AB is divided into two equal parts in the point D. PROPOSITION XI . PROBLEM . To draw a straight line at right angles ...
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.