Elements of Plane Geometry According to EuclidW. and R. Chambers, 1837 - 240 σελίδες |
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Σελίδα ix
... problems . This knowledge might have been attained , however , only by shrewd conjec- ture or tentative mechanical methods , instead of logical reasoning . The opinions regarding the origin of geometry are various , but they concur in ...
... problems . This knowledge might have been attained , however , only by shrewd conjec- ture or tentative mechanical methods , instead of logical reasoning . The opinions regarding the origin of geometry are various , but they concur in ...
Σελίδα x
... problem of the Duplication of the Cube depends upon the finding of two mean proportionals ; a question which arose from the request of the oracle at Delos to double the cubic altar of Apollo . He was the second who composed a treatise ...
... problem of the Duplication of the Cube depends upon the finding of two mean proportionals ; a question which arose from the request of the oracle at Delos to double the cubic altar of Apollo . He was the second who composed a treatise ...
Σελίδα xi
... problem of two mean proportionals . Di- nostratus discovered a property of the Quadratrix , a curve which was no doubt invented for the purpose of solving the problem of the trisection of an angle , and the invention of which is ...
... problem of two mean proportionals . Di- nostratus discovered a property of the Quadratrix , a curve which was no doubt invented for the purpose of solving the problem of the trisection of an angle , and the invention of which is ...
Σελίδα xii
... problems . Archimedes ( born 287 B. c . ) was the most celebrated of all the ancient mathematicians . He enjoyed the most extensive , and also the most popular reputation ; for to his abstract researches he added several striking ...
... problems . Archimedes ( born 287 B. c . ) was the most celebrated of all the ancient mathematicians . He enjoyed the most extensive , and also the most popular reputation ; for to his abstract researches he added several striking ...
Σελίδα xiv
... problem that required considerable skill . Menalaus ( second cen- tury ) was the author of a treatise on ... problem . Eutocius also gives the former the credit of solving the problem of Archimedes respecting the section of a hemisphere ...
... problem that required considerable skill . Menalaus ( second cen- tury ) was the author of a treatise on ... problem . Eutocius also gives the former the credit of solving the problem of Archimedes respecting the section of a hemisphere ...
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.