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].1834 |
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Página v
... likewise is of the greatest use in the arts both of peace and war , to many of which geometry is absolutely necessary . This I have endeavoured to do , by taking away the inaccurate and false reasonings which unskilful editors have put ...
... likewise is of the greatest use in the arts both of peace and war , to many of which geometry is absolutely necessary . This I have endeavoured to do , by taking away the inaccurate and false reasonings which unskilful editors have put ...
Página viii
... likewise applied himself to the study of mixed mathema- tics , particularly to astronomy and optics . His works , as we learn from Pappus and Proclus , are the Elements , Data , Introduction to Harmony , Phænomena , Op- tics ...
... likewise applied himself to the study of mixed mathema- tics , particularly to astronomy and optics . His works , as we learn from Pappus and Proclus , are the Elements , Data , Introduction to Harmony , Phænomena , Op- tics ...
Página 7
... likewise equal to † AD ; whence † Constr . AE and C are each of them equal to AD ; wherefore , the straight line AE ... likewise the angles contained by those sides equal to one another , they shall likewise have their bases , or third ...
... likewise equal to † AD ; whence † Constr . AE and C are each of them equal to AD ; wherefore , the straight line AE ... likewise the angles contained by those sides equal to one another , they shall likewise have their bases , or third ...
Página 8
... likewise be equal ; and the triangles shall be equal , and their other angles , to which the equal sides are opposite , shall be equal , each to each . Which was to be de- monstrated . PROPOSITION V. PONS A SYNORUM . THEOR . - The ...
... likewise be equal ; and the triangles shall be equal , and their other angles , to which the equal sides are opposite , shall be equal , each to each . Which was to be de- monstrated . PROPOSITION V. PONS A SYNORUM . THEOR . - The ...
Página 10
... likewise those which are terminated in the other ex- tremity . If it be possible , upon the same base AB , and upon the same side of it , let there be two triangles ACB , ADB , which have their sides CA , DA , terminated in the ...
... likewise those which are terminated in the other ex- tremity . If it be possible , upon the same base AB , and upon the same side of it , let there be two triangles ACB , ADB , which have their sides CA , DA , terminated in the ...
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Términos y frases comunes
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circle EFGH circumference common logarithm cone Constr 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 gnomon greater join less Let ABC logarithm multiple parallel parallelogram perpendicular point F polygon prism Prop proportionals Q. E. D. PROPOSITION radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR.-If tiple triangle ABC vertex wherefore
Pasajes populares
Página 32 - To a given straight line, to apply a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle...
Página 138 - 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 39 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Página 41 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Página 38 - IF a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided...
Página 262 - 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 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...
Página 165 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.