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 29
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Σελίδα 40
... reason EF is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the whole , or the remain- c 2. or 3. der AE , is equal to the whole , or the remainder DF ; AB also is equal to DC ; and the two EA , AB are ...
... reason EF is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the whole , or the remain- c 2. or 3. der AE , is equal to the whole , or the remainder DF ; AB also is equal to DC ; and the two EA , AB are ...
Σελίδα 41
... reason , the parallelogram EFGH is equal to the same EBCH : therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
... reason , the parallelogram EFGH is equal to the same EBCH : therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
Σελίδα 45
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AFK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AFK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
Σελίδα 49
... reason , AB and AH are in the same straight line ; and because the angle DBC is e- qual to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole angle DBA is equal to the whole FBC ; and because ...
... reason , AB and AH are in the same straight line ; and because the angle DBC is e- qual to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole angle DBA is equal to the whole FBC ; and because ...
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.