Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 σελίδες |
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Σελίδα xxii
... fourth century . Her father , perceiving her ex- traordinary genius , had her not only educated in all the ordinary accomplishments of her sex , but instructed in the most abstruse sciences . She made such great progress in philosophy ...
... fourth century . Her father , perceiving her ex- traordinary genius , had her not only educated in all the ordinary accomplishments of her sex , but instructed in the most abstruse sciences . She made such great progress in philosophy ...
Σελίδα xxiii
... fourth century , in the reign of Theodosius the Great many of his works are lost , or lie in the hitherto unexplored recesses of public libraries ; Suidas mentioned many of them , as also Vossius de Scientiis Mathematicis : amongst ...
... fourth century , in the reign of Theodosius the Great many of his works are lost , or lie in the hitherto unexplored recesses of public libraries ; Suidas mentioned many of them , as also Vossius de Scientiis Mathematicis : amongst ...
Σελίδα 12
... fourth , although Euclid has not added so much as in that theorem , viz . , that the triangles and remaining angles are equal ; the reason is manifest , for the equality of the vertical angles being demonstrated , it follows , that all ...
... fourth , although Euclid has not added so much as in that theorem , viz . , that the triangles and remaining angles are equal ; the reason is manifest , for the equality of the vertical angles being demonstrated , it follows , that all ...
Σελίδα 115
... fourth , the first is said to have to the second the same ratio that the third has to the fourth . " " 3. If the first of four magnitudes be greater , when compared to the 4. Magnitudes are said to have a proportion to one 12 EUCLID'S ...
... fourth , the first is said to have to the second the same ratio that the third has to the fourth . " " 3. If the first of four magnitudes be greater , when compared to the 4. Magnitudes are said to have a proportion to one 12 EUCLID'S ...
Σελίδα 116
... fourth , the first is said to have to the second a greater ratio than the third has to the fourth . " " 4. If the first of four magnitudes be less , when compared to the second , than the third is when compared to the fourth , the first ...
... fourth , the first is said to have to the second a greater ratio than the third has to the fourth . " " 4. If the first of four magnitudes be less , when compared to the second , than the third is when compared to the fourth , the first ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry; Containing the First Six Books of Euclid ... Euclid,John Playfair Πλήρης προβολή - 1814 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles Algebra angle ABC angle ACB angle BAC angles equal base BC bisected centre circle ABC circum circumference BC diameter double draw equal angles equal circles equal right lines equal to F equi equiangular equimultiples Euclid EUCLID'S ELEMENTS exceed exterior angle fore four magnitudes fourth Geometry given circle given point given right line gnomon greater ratio hence inscribed join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deduction Q. E. D. PROPOSITION rectangle contained remaining angle right angles right line AB right line AC sector HEF segment side BC similar and similarly square of AC subtending THEOREM tiple touches the circle triangle ABC triangle DEF whence whole
Δημοφιλή αποσπάσματα
Σελίδα xxvi - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Σελίδα 148 - 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 27 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Σελίδα 8 - 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 73 - DH; (I. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same thing, however great an acute angle a straight line makes with the diameter at the point A, or however small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE.
Σελίδα 99 - To describe a square about a given circle. Let ABCD be the given circle ; it is required to describe a square about it. . Draw two diameters AC, BD of the circle ABCD, at right angles to one another, and through the points A, B, • 17.3. C, D, draw...
Σελίδα 7 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Σελίδα 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.