The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthR. and A. Foulis, 1762 - 466 σελίδες |
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Αποτελέσματα 1 - 5 από τα 52.
Σελίδα 43
... faid to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a diameter , together with the two com- plements , is called a Gno- mon . Thus ...
... faid to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a diameter , together with the two com- plements , is called a Gno- mon . Thus ...
Σελίδα 59
... faid to touch one another , which meet but do not cut one another . IV . Straight lines are faid to be equally diftant from the center of a circle , when the perpendiculars drawn to them from the center are equal , V. And the straight ...
... faid to touch one another , which meet but do not cut one another . IV . Straight lines are faid to be equally diftant from the center of a circle , when the perpendiculars drawn to them from the center are equal , V. And the straight ...
Σελίδα 60
... faid to infift or stand upon the circumference intercepted be- tween the straight lines that contain the angle . X. The sector of a circle is the figure con- tained by two straight lines drawn from the center , and the circumference be ...
... faid to infift or stand upon the circumference intercepted be- tween the straight lines that contain the angle . X. The sector of a circle is the figure con- tained by two straight lines drawn from the center , and the circumference be ...
Σελίδα 72
... faid to be e qually diftant from the center , when the perpendiculars drawn to them from C G F E D 4. Def . 3. the center are equal . therefore AB , A CD are equally diftant from the center . Next , if the straight lines AB , CD be ...
... faid to be e qually diftant from the center , when the perpendiculars drawn to them from C G F E D 4. Def . 3. the center are equal . therefore AB , A CD are equally diftant from the center . Next , if the straight lines AB , CD be ...
Σελίδα 74
... faid to be greater than any acute rectilineal angle , and the re- ' maining angle less than any rectilineal angle . ' COR . From this it is manifeft that the straight line which is drawn at right angles to the diameter of a circle from ...
... faid to be greater than any acute rectilineal angle , and the re- ' maining angle less than any rectilineal angle . ' COR . From this it is manifeft that the straight line which is drawn at right angles to the diameter of a circle from ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated drawn equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fame reaſon fecond fegment fhall fhewn fides fimilar firft firſt folid angle fome fore fquare of BC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs Let ABC likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular polygon prifms Propofition proportionals pyramid Q. E. D. PROP reafon rectangle rectangle contained rectilineal figure right angles ſhall ſphere ſquare ſtraight line AB thefe THEOR theſe thro tiple triangle ABC wherefore
Δημοφιλή αποσπάσματα
Σελίδα 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 163 - 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 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Σελίδα 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.