The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson].1814 |
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Página 60
Euclides Robert Simson. BOOK III . VI . A segment of a circle is the figure contained by a straight line and the circumference it cuts off . VII . " The angle of a segment is that which is contained by the " straight line and the ...
Euclides Robert Simson. BOOK III . VI . A segment of a circle is the figure contained by a straight line and the circumference it cuts off . VII . " The angle of a segment is that which is contained by the " straight line and the ...
Página 61
... circle ABC : Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . IF any PROP . II . THEOR . two ...
... circle ABC : Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . IF any PROP . II . THEOR . two ...
Página 63
... a straight line , & c . Q. E. D. PROP . IV . THEOR . IF in a circle two straight lines cut one another which do not both pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in ...
... a straight line , & c . Q. E. D. PROP . IV . THEOR . IF in a circle two straight lines cut one another which do not both pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in ...
Página 64
... circle ABC , CE is equal to EF : Again , A // D because E is the centre of the cir- cle CDG , CE is equal to EG : But CE was shown to be equal to EF ; therefore EF is equal to EG , the less to the greater , which is impossible ...
... circle ABC , CE is equal to EF : Again , A // D because E is the centre of the cir- cle CDG , CE is equal to EG : But CE was shown to be equal to EF ; therefore EF is equal to EG , the less to the greater , which is impossible ...
Página 65
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre : Let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre : Let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Visualização integral - 1834 |
Palavras e frases frequentes
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm meet multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Passagens conhecidas
Página 3-7 - 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.
Página 16 - Any two sides of a triangle are together greater than the third side.
Página 26 - 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.
Página 16 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Página 304 - 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.
Página 4 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.
Página 147 - 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.
Página 3-16 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.