They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real algebra, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being called res and its square census.
The metaphysical and theological conception is open to the agnostic objection that the finite mind of man is by hypothesis unable to cognize or apprehend not only an infinite object, but even the very conception of infinity itself; from this standpoint the infinite is regarded as merely a postulate, as it were an unknown quantity (cf.
The distinction between algebraical and arithmetical reasoning then lies mainly in the fact that the former is in a more condensed form than the latter; an unknown quantity being represented by a special symbol, and other symbols being used as a kind of shorthand for verbal expressions.
In the Flos equations with negative values of the unknown quantity are also to be met with, and Leonardo perfectly understands the meaning of these negative solutions.
This problem is only solvable if we cease arbitrarily to substitute for the unknown x itself the conditions under which that force becomes apparent--such as the commands of the general, the equipment employed, and so on--mistaking these for the real significance of the factor, and if we recognize this unknown quantity in its entirety as being the greater or lesser desire to fight and to face danger.
His publications include The Reality of Religion (1884); The Poetry of Tennyson (1889); The Other Wise Man (1896); Ships and Havens (1897); The Toiling of Felix, and Other Poems (1900); The Poetry of the Psalms (1900); The Blue Flower (1902); Days Off (1907); The House of Rimmon (1908); Out-of-Doors in the Holy Land (1908); Collected Poems (191 I); The Bad Shepherd (1911); The Unknown Quantity (1912); The Lost Boy (1914); Fighting for Peace (1917); The Valley of Vision (1919); and Golden Stars (1919) .
If men descended from the apes at an unknown period of time, that is as comprehensible as that they were made from a handful of earth at a certain period of time (in the first case the unknown quantity is the time, in the second case it is the origin); and the question of how man's consciousness of freedom is to be reconciled with the law of necessity to which he is subject cannot be solved by comparative physiology and zoology, for in a frog, a rabbit, or an ape, we can observe only the muscular nervous activity, but in man we observe consciousness as well as the muscular and nervous activity.
In determinations of stellar or solar parallax, comparison stars, symmetrically situated with respect to the object whose parallax is sought, should be employed, in which case the instantaneous scale-value may be regarded as an unknown quantity which can be derived in the process of the computation of the results.
This condition is represented in the algebraic theory when we have one more unknown quantity than the number of equations; i.e.
That unknown quantity is the spirit of the army, that is to say, the greater or lesser readiness to fight and face danger felt by all the men composing an army, quite independently of whether they are, or are not, fighting under the command of a genius, in two--or three-line formation, with cudgels or with rifles that repeat thirty times a minute.