The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthDesilver, Thomas & Company, 1838 - 416 sider |
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Resultat 1-5 av 91
Side 3
... given of compound ratio , and giving an absurd one in place of it , in the 5th Definition of the 6th Book , which ... given , is put in its proper place among the Definitions of the 5th Book , by which the doctrine of compound ratios is ...
... given of compound ratio , and giving an absurd one in place of it , in the 5th Definition of the 6th Book , which ... given , is put in its proper place among the Definitions of the 5th Book , by which the doctrine of compound ratios is ...
Side 149
... given rectilineal C , exceeding by the parallelogram PO , which is similar to D , because PŎ is similar to EL ( 24. 6. ) . Which was to be done . PROP . XXX . PROB . To cut a given straight line in extreme and mean ratio . Let AB be the ...
... given rectilineal C , exceeding by the parallelogram PO , which is similar to D , because PŎ is similar to EL ( 24. 6. ) . Which was to be done . PROP . XXX . PROB . To cut a given straight line in extreme and mean ratio . Let AB be the ...
Side 240
... give the reason why two sides of a triangle are greater than the third : but the ... ratio which is less than that of two to one , as Pappus Alexandrinus has ... given , viz . that any two of the straight lines DF , FG , GH , must be ...
... give the reason why two sides of a triangle are greater than the third : but the ... ratio which is less than that of two to one , as Pappus Alexandrinus has ... given , viz . that any two of the straight lines DF , FG , GH , must be ...
Side 249
... give a general and summary idea of ratio to beginners , by premising this metaphysical definition , to the more accurate definitions of ratios that are the same to one another , or one of which is greater , or less than the other ; I ...
... give a general and summary idea of ratio to beginners , by premising this metaphysical definition , to the more accurate definitions of ratios that are the same to one another , or one of which is greater , or less than the other ; I ...
Side 250
... proportion of numbers to one another is defined , and treated of , yet without giving any definition of the ratio of num- bers ; though such a definition was as necessary and useful to be given in that book , as in this : but indeed ...
... proportion of numbers to one another is defined , and treated of , yet without giving any definition of the ratio of num- bers ; though such a definition was as necessary and useful to be given in that book , as in this : but indeed ...
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference Co-S cone 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 join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 41 - 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.
Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 256 - 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.
Side 129 - 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.
Side 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 20 - ANY two angles of a triangle are together less than two right angles.