The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Page 1
... drawn . ' This shows that every straight line in the Elements is considered to be of indefinite length , unless otherwise expressed . V. A superficies is that which hath only length and breadth . A superficies or surface , is extension ...
... drawn . ' This shows that every straight line in the Elements is considered to be of indefinite length , unless otherwise expressed . V. A superficies is that which hath only length and breadth . A superficies or surface , is extension ...
Page 3
... drawn from the centre to the circumference , is called the radius . XVII . A diameter of a circle is a straight line drawn through the centre , anc terminated both ways by the circumference . XVIII . A semicircle is the figure contained ...
... drawn from the centre to the circumference , is called the radius . XVII . A diameter of a circle is a straight line drawn through the centre , anc terminated both ways by the circumference . XVIII . A semicircle is the figure contained ...
Page 5
... drawn from any one point to any other point . When a straight line is drawn from one point to another point , the points are said to be joined . The points are understood to be in the same plane . II . That a terminated straight line ...
... drawn from any one point to any other point . When a straight line is drawn from one point to another point , the points are said to be joined . The points are understood to be in the same plane . II . That a terminated straight line ...
Page 7
... draw the straight lines ( Post . 1 ) CA , CB , to the points A , B. Then ABC is an equilateral triangle . D E Because ... drawn equal to the given straight line B C. K TT D G F equal to the a straight line Q. E. F. The construction of ...
... draw the straight lines ( Post . 1 ) CA , CB , to the points A , B. Then ABC is an equilateral triangle . D E Because ... drawn equal to the given straight line B C. K TT D G F equal to the a straight line Q. E. F. The construction of ...
Page 13
... draw a straight line from the point C at right angles to AB . Take any point D in AC , and make ( I. 3 ) CE equal to ČD . Upon DE describe ( I. 1 ) the equilateral triangle DFE , and join FC . The straight line FC drawn from the given ...
... draw a straight line from the point C at right angles to AB . Take any point D in AC , and make ( I. 3 ) CE equal to ČD . Upon DE describe ( I. 1 ) the equilateral triangle DFE , and join FC . The straight line FC drawn from the given ...
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The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides No preview available - 2016 |
Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle DEF angle EDF base BC bisected centre circle ABC circumference cone cylinder described diagonal diameter draw duplicate ratio equal angles equal Ax equal Const equiangular equimultiples Euclid ex æquali Exercise exterior angle fore given straight line gnomon homologous sides inscribed join less meet multiple opposite angle parallelogram parallelogram AC parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP reciprocally proportional rectangle contained rectilineal figure remaining angle right angles segment similar triangles solid angle sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines triangle ABC triangle DEF triplicate ratio twice the rectangle vertex Wherefore whole angle
Popular passages
Page 23 - 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.
Page 34 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 2 - 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.
Page 122 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Page 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Page 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Page 37 - 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...