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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Αποτελέσματα 6 - 10 από τα 99.
Σελίδα 23
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance CD ...
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance CD ...
Σελίδα 26
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACĎ is greater than either of the interior op- posite angles CBA ...
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACĎ is greater than either of the interior op- posite angles CBA ...
Σελίδα 28
... Produce BA to the point D , and make a AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal to ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the ...
... Produce BA to the point D , and make a AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal to ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the ...
Σελίδα 34
... produced do not meet towards B , D. In like man- C. ner it may be demonstrat- E B G F D ed that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so b 35. Def . far , are parallel b ...
... produced do not meet towards B , D. In like man- C. ner it may be demonstrat- E B G F D ed that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so b 35. Def . far , are parallel b ...
Σελίδα 35
... produced ; therefore 12. ax . the straight lines AB , CD , if produced far enough , shall meet ; See the but they never meet , since they are parallel by the hypothesis ; notes on therefore the angle AGH is not unequal to the angle GHD ...
... produced ; therefore 12. ax . the straight lines AB , CD , if produced far enough , shall meet ; See the but they never meet , since they are parallel by the hypothesis ; notes on therefore the angle AGH is not unequal to the angle GHD ...
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.