The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 pages |
From inside the book
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Page 3
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another . P XVI . And this point is called the centre of the circle . XVII . A diameter of a ...
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another . P XVI . And this point is called the centre of the circle . XVII . A diameter of a ...
Page 58
... circumference it cuts off . VII . D " The angle of a segment is that which is contained by the " straight line and the circumference . " VIII . An angle in a segment is the angle con- tained by two straight lines drawn from any point ...
... circumference it cuts off . VII . D " The angle of a segment is that which is contained by the " straight line and the circumference . " VIII . An angle in a segment is the angle con- tained by two straight lines drawn from any point ...
Page 59
... circumference of a circle , the straight line which joins them must fall within the circle . Let ABC be a circle , and A , B any two points in the circum- ference ; the straight line drawn from A to B must fall within the circle . For ...
... circumference of a circle , the straight line which joins them must fall within the circle . Let ABC be a circle , and A , B any two points in the circum- ference ; the straight line drawn from A to B must fall within the circle . For ...
Page 60
... circumference : it falls therefore within it . Wherefore , " if any two points , " & c . Q. E. D. PROP . III . THEOR . If a straight line drawn through the centre of a circle bisect a straight line in the circle , which does not pass ...
... circumference : it falls therefore within it . Wherefore , " if any two points , " & c . Q. E. D. PROP . III . THEOR . If a straight line drawn through the centre of a circle bisect a straight line in the circle , which does not pass ...
Page 63
... circumference , the great- est is that in which the centre is , and the other part of that diameter is the least ; and , of any others , that which is nearer to the line passing through the centre is always greater than one more remote ...
... circumference , the great- est is that in which the centre is , and the other part of that diameter is the least ; and , of any others , that which is nearer to the line passing through the centre is always greater than one more remote ...
Other editions - View all
The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given ABCD altitude angle ABC angle BAC arch base BC BC is equal bisected Book XI centre circle ABC circumference cone cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
Popular passages
Page 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Page 306 - 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.
Page 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Page 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Page 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Page 153 - 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.
Page 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Page 28 - 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.
Page 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Page 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...