The Elements of Euclid: Viz. the First Six Books, with the Eleventh and Twelfth. In which the Corrections of Dr. Simson are Generally Adopted, But the Errors Overlooked by Him are Corrected, and the Obscurities of His and Other Editions Explained. Also Some of Euclid's Demonstrations are Restored, Others Made Shorter and More General, and Several Useful Propositions are Added. Together with Elements of Plane and Spherical Trigonometry, and a Treatise on Practical GeometryJ. Pillans & sons, 1799 - 351 σελίδες |
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Σελίδα 16
... base of an Ifofceles triangle are equal to one another ; and , if the equal fides be produced , the angles upon the other fide of the base Thall be equal . Let ABC be an Ifofceles triangle , of which the fide AB is equal to AC , and let ...
... base of an Ifofceles triangle are equal to one another ; and , if the equal fides be produced , the angles upon the other fide of the base Thall be equal . Let ABC be an Ifofceles triangle , of which the fide AB is equal to AC , and let ...
Σελίδα 17
... base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal b to the remaining angles of the other , each to each , to which the equal fides are oppofite , viz . the angle ACF to the angle ABG ...
... base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal b to the remaining angles of the other , each to each , to which the equal fides are oppofite , viz . the angle ACF to the angle ABG ...
Σελίδα 18
... base , and on the fame fide of it , that have their fides , which are terminated in one extremity of the base equal to one another , they shall not have their fides equal , which are terminated in the other extremity . Let there be two ...
... base , and on the fame fide of it , that have their fides , which are terminated in one extremity of the base equal to one another , they shall not have their fides equal , which are terminated in the other extremity . Let there be two ...
Σελίδα 19
... base EF , but the fides BA , CA do not coincide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame base EF , and upon the fame fide of it , there can be two triangles that have their fides ...
... base EF , but the fides BA , CA do not coincide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame base EF , and upon the fame fide of it , there can be two triangles that have their fides ...
Σελίδα 20
... base c DB , and the ftraight line AB is divided into two equal parts in the point D. Which A was to be done . PROP ... base DF is also equal to the base EF ; therefore the angle DCF is equal to the angle C ECF ; F ECF ; and they are ...
... base c DB , and the ftraight line AB is divided into two equal parts in the point D. Which A was to be done . PROP ... base DF is also equal to the base EF ; therefore the angle DCF is equal to the angle C ECF ; F ECF ; and they are ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifect Book XI cafe centre circle ABC circumference cofine confequently cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid exterior angle faid fame altitude fame manner fame multiple fame number fame ratio fame reaſon fecond fegment fhall fides fimilar firft firſt folid angle fome fore fquare fquare of AC fuperficies given ftraight line gnomon greater half the fum join lefs leſs Let ABC magnitudes meaſure oppofite angle pafs parallel parallelogram parallelopiped perpendicular plane angles prifm PROB propofition proportionals Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſhall ſquare tangent thefe THEOR theſe tiple triangle ABC Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 142 - 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 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 30 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Σελίδα 72 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Σελίδα 57 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Σελίδα 145 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Σελίδα 48 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 35 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 10 - 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.