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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Σελίδα
... magnitude . " Now this Proposition is a Theorem , not a Definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and therefore , though this were a true proposition , it ought to have been ...
... magnitude . " Now this Proposition is a Theorem , not a Definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and therefore , though this were a true proposition , it ought to have been ...
Σελίδα 111
... magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a certain number of times ' exactly . ' " III . ' Ratio is a mutual relation of two magnitudes of the ...
... magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a certain number of times ' exactly . ' " III . ' Ratio is a mutual relation of two magnitudes of the ...
Σελίδα 112
... magnitude has to the fourth ; and , on the contrary , the third is said to have to the fourth a less ratio than the ... magnitude . For example , if A , B , C , D , be four magnitudes of the same kind , the first A is said to have to the ...
... magnitude has to the fourth ; and , on the contrary , the third is said to have to the fourth a less ratio than the ... magnitude . For example , if A , B , C , D , be four magnitudes of the same kind , the first A is said to have to the ...
Σελίδα 113
... magnitude of proportionals , so as that they continue still to be proportionals . ' 6 XIII . Permutando , or alternando , by permutation , or alternately . This word is used when there are four proportionals , and See N. it is inferred ...
... magnitude of proportionals , so as that they continue still to be proportionals . ' 6 XIII . Permutando , or alternando , by permutation , or alternately . This word is used when there are four proportionals , and See N. it is inferred ...
Σελίδα 114
... magnitudes are taken , ' two and two . ' XIX . Ex æquali , from equality . This term is used simply by it- self , when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and as the ...
... magnitudes are taken , ' two and two . ' XIX . Ex æquali , from equality . This term is used simply by it- self , when the first magnitude is to the second of the first rank , as the first to the second of the other rank ; and as the ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 16 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.