The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedConrad and Company, 1810 - 518 σελίδες |
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Σελίδα 25
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. in the same straight line with it ; therefore , because the straight Book I. line AB makes angles with the straight line CBE , upon one s ...
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. in the same straight line with it ; therefore , because the straight Book I. line AB makes angles with the straight line CBE , upon one s ...
Σελίδα 28
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. Book I. but it is not ; therefore the side AC is not less than AB ; and it has been shown that it is not equal to AB ; therefore AC is ...
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. Book I. but it is not ; therefore the side AC is not less than AB ; and it has been shown that it is not equal to AB ; therefore AC is ...
Σελίδα 44
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. Book I. Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE ; the ...
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. Book I. Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE ; the ...
Σελίδα 45
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. FECG equal to a given triangle ABC , having one of its angles Book I CEF equal to the given angle D. Which was to be done . PROP . XLIII ...
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. FECG equal to a given triangle ABC , having one of its angles Book I CEF equal to the given angle D. Which was to be done . PROP . XLIII ...
Σελίδα 69
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. For , if it be not , let , if possible , G be the centre , and join Book III . GA , GD , GB : then , because DA is equal to DB , and DG c ...
... Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Cor Euclid. For , if it be not , let , if possible , G be the centre , and join Book III . GA , GD , GB : then , because DA is equal to DB , and DG c ...
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of BC rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 17 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.
Σελίδα 35 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 67 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Σελίδα 92 - IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 26 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made of the whole and that part.
Σελίδα 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 22 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 161 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα 21 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.