Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 σελίδες |
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Αποτελέσματα 1 - 5 από τα 22.
Σελίδα 30
... half the difference between the vertical angle and two right angles . 2. The difference of the angles at the base of any triangle is double the angle contained by the line bisecting the vertical angle and another drawn from the vertex ...
... half the difference between the vertical angle and two right angles . 2. The difference of the angles at the base of any triangle is double the angle contained by the line bisecting the vertical angle and another drawn from the vertex ...
Σελίδα 34
... half of the parallelogram EBCA , because the diameter AB bisects it ; and the triangle DBC is half of the parallelogram DBCF , for the diameter DC bisects it . But the halves of equal things are equal . Therefore the triangle ABC is ...
... half of the parallelogram EBCA , because the diameter AB bisects it ; and the triangle DBC is half of the parallelogram DBCF , for the diameter DC bisects it . But the halves of equal things are equal . Therefore the triangle ABC is ...
Σελίδα 36
... altitude being given ; for as the area of a parallelogram is the product of the base and altitude , it follows that the area of a triangle must be half that product , d ს b с d 31. 1 . angle CEF 36 [ Book 1 . EUCLID'S ELEMENTS .
... altitude being given ; for as the area of a parallelogram is the product of the base and altitude , it follows that the area of a triangle must be half that product , d ს b с d 31. 1 . angle CEF 36 [ Book 1 . EUCLID'S ELEMENTS .
Σελίδα 37
... half of the given one , and the diameters of this parallelogram shall be equal to half of the perimeter of the other . PROPOSITION XLIII . THEOREM . The complements of any parallelogram which are about the diameter of any parallelogram ...
... half of the given one , and the diameters of this parallelogram shall be equal to half of the perimeter of the other . PROPOSITION XLIII . THEOREM . The complements of any parallelogram which are about the diameter of any parallelogram ...
Σελίδα 49
... half the line . The same by Algebra . 2 Put a equal to the right line AB , and suppose it divided into any two parts f , g ; then shall a = ƒ2 + 2 fgg . For a * = ƒ + g square each side , and we * Ax . 8. 1 . shall have a2 = ƒ2 + 2ƒg + ...
... half the line . The same by Algebra . 2 Put a equal to the right line AB , and suppose it divided into any two parts f , g ; then shall a = ƒ2 + 2 fgg . For a * = ƒ + g square each side , and we * Ax . 8. 1 . shall have a2 = ƒ2 + 2ƒg + ...
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.