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 sider |
Inni boken
Resultat 6-10 av 35
Side 51
... double of AK : But twice the rectangle AB , BC is double of AK , for BK is equal c to BC : Therefore the gnomon AKF , together with the fquare CK , is D equal to twice the rectangle AB , BC : To each of these equals add HF , which is ...
... double of AK : But twice the rectangle AB , BC is double of AK , for BK is equal c to BC : Therefore the gnomon AKF , together with the fquare CK , is D equal to twice the rectangle AB , BC : To each of these equals add HF , which is ...
Side 53
... double of the fquare of half the line , and of the fquare of the line between the points of fection . Let the ftraight line AB be divided at the point C into two equal , and at D into two unequal parts : The fquares of AD , DB are ...
... double of the fquare of half the line , and of the fquare of the line between the points of fection . Let the ftraight line AB be divided at the point C into two equal , and at D into two unequal parts : The fquares of AD , DB are ...
Side 54
... double of the fquare of AC ; therefore the fquares of AE , EF are double of the fquares of AC , CD : And the fquare of AF is equal to the fquares of AE , EF , because AEF is a right angle ; therefore the fquare of AF is double of the ...
... double of the fquare of AC ; therefore the fquares of AE , EF are double of the fquares of AC , CD : And the fquare of AF is equal to the fquares of AE , EF , because AEF is a right angle ; therefore the fquare of AF is double of the ...
Side 58
... double of BE , and BC double of BD ; the remainder CF is double of the remainder DE : And because BF is divided into two equal parts in the point E , and into two unequal parts in the point C ; the rectangle BC . CF , together with the ...
... double of BE , and BC double of BD ; the remainder CF is double of the remainder DE : And because BF is divided into two equal parts in the point E , and into two unequal parts in the point C ; the rectangle BC . CF , together with the ...
Side 59
... double of the fquares of BD , DA . A a 10. I. C d 9.2 . If the angles at D be right angles , the fquare of BA is equal b to the fquares of BD , DA , and the fquare of AC to the fquares b 47. I. of CD , DA , or of BD , DA ; therefore the ...
... double of the fquares of BD , DA . A a 10. I. C d 9.2 . If the angles at D be right angles , the fquare of BA is equal b to the fquares of BD , DA , and the fquare of AC to the fquares b 47. I. of CD , DA , or of BD , DA ; therefore the ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.