THE HISTORY OF 



J87 



(8.) Multiply a -f 1 + <? ab ac be by a + b -f r. 

 . J + /--f-c s 3aic. 



thi- i.riiu-i].l.-i explained in Articles C6 to 89 wo derive 

 lowing general rule for multiplication : 

 MI. RULE. Multiply tlw letters and co-efficients of ca 

 'i-iind l"j tin /liters and co-efficients of each ' 

 '/i/i/iVi- ; cm/ i>i--ji.i In each term of tlie product the sign 

 ,-inciple, (luit l&e siyns produce -)- , an" 



,' similar. 



otlirrv. i.-r. M' ' jini't i if tin' multiplicand by eoery 



pwt uf lie ' the results as in addition. 



ILXERCISE 6. 



1 . Sal X 3oi/. 



2. n H x un - '. 

 8. flta + * x v" - P. 



5. a x tfl. 



0. z*y* x 3~>y. 



7. t s - 3** + :t. 



8. 1 - 2* + 3* - -!J3 x 1 + r. 



9. *a + 2oz + a* x ^ 2a.c + a. 



10. - 3z. 



11. Multiply a -i- 3b - 2 into 4a - Cb - 4. 



12. Multiply -hil x x x 2 into 3my - 1 + h. 



13. Multiply (Tuft - y) x -i into 4z x 3 x 5 x d. 



14. Multiply (6<ib - Jid + 1) x 2 into (8 + 4x - 1) x d. 



15. Multiply 3ay + y - -i + h into (a + *) x (7i + y). 



16. Multiply Co* - (4h - d) iuto (b + 1) x (h + 1). 



17. Required the continual product of a + b-fc, a + b + e,al 

 * c, and a + 6 c. 



18. Find the product of x* - \? + z 3 - v* x ** + i/ - & - ,-. 



19. Find the continual product of 2r y, 2x + y, and -U- + -y s . 



20. Multiply a + b into a + b into a + b. 



21. Multiply x + y into x y into * + y. 



22. Multiply 4 (x + y) into 3a into Cb into 3. 



23. Multiply 3 (a + b + c + d) into xyz. 



24. Multiply rx + ry -i- i/ij into a- - y. 



25. Multiply aaa, bbb into ana, + l>bb. 



26. Multiply aa ax + xx into a + a-. 



27. Multiply i/yy nyij T ncy <wa into y + a. 



28. Multiply 15o + 20bb into 3a - 4bb. 



29. Multiply 3a (x + i/) x 4 into <i + b. 



30. Multiply aa + 2ab + bb into a + b into a + b. 



31. Find tho product of x - 2r< + ar' x 4.1- 4 + M$ - Gx". 



32. Find the product of 5y" - 7>/* - S;, 3 + 3y + y x 7y - 8. 



33. Find the product of a3 2a* + 3 x a' + 2a - ::. 



34. Find the product of t>* - 4ar s + GaV - 4a s u + a* x & - Sac 2 + 3a2r 

 -a. 



33. Find the product of x a - a'.c + 2a x ** ax + 2u*. 



36. Find the continual product of x 1, x + 2, .t + 4, and x 5. 



37. Multiply 1 - x + ** - a 3 + x* - c 5 by 1 + .r + x 1 . 



of the people for whom they painted. Holland in not a land of 

 any natural sublimity in any way : it ha* no great mountain*, 

 no vast rocks, no waterfall*, no forest*, and no magnificent 

 scenery of any sort. Thus, in the matter of landscape, Dntch 

 painters have been necessarily restricted to the ordinary flat 

 and somewhat dull feature* of the country aa seen 

 Quaint old towns, with tall, brick-fronted houses ; canal 



THE HISTORY OF ART. 



XIV. THE BUTCH SCHOOL. 



HOLLAND is the land of toilsome and painstaking labour, the 

 masterpiece of man's victory over the brute forces of nature. 

 The soil itself in many places has been won from the sea by a 

 laborious system of dykes and ramparts ; and it is only pre- 

 served for its inhabitants by ceaseless and unremitting watch- 

 fulness. All the mental characteristics of the Dutch have been 

 begotten by the peculiar circumstances under which they live. 

 The care they have to exercise in merely keeping out the ever- 

 oncroaching sea ; the pains they require in pumping and draining 

 their land ; the minute patience needed in merely guarding and 

 cultivating their soil all these things have reacted generation 

 after generation on the national mind, and have made the Dutch 

 the most frugal, industrious, and ingenious nation in Europe. 

 The same causes have led to a general spread of wealth and 

 well-being throughout the masses in Holland : everybody is 

 fairly well off, and everybody lives in a style of much comfort 

 and ease, and even in some simple luxury. Hence Dutch art 

 has always taken a peculiarly democratic and domestic turn. 

 It has grown up among the people themselves, not among a 

 small aristocratic class; and it has busied itself about the 

 subjects in which the people as a whole feel a personal interest. 

 All Dutch painting is very minute, painstaking, and careful 

 of detail. The artists have been trained in a school of life 

 whore they learnt to do everything with much exactness. Their 

 subjects have been defined for them to a great extent by the 

 nature of the country, and to a great extent also by the nature 



with tall poplars, and overlooked by stately yet homely : 

 sions ; flat fields and roads, with little comical Dutch churches ; 

 everything trim and neat and quiet, with a certain formal 

 prettiness of its own, but no pretence to grandeur in any way 

 thin is what we get in the ordinary landscape painting of the 

 Netherlands. Historical i>i>:tur<-H of the usual grandiose type 

 are also almost unknown ; for Holland has had little history of 

 the common sort, and what history it has had has not been of a 

 very pictorial character. 



Again, the style of art demanded by the Dntch people wa* 

 one of a peculiarly domestic and somewhat undignified kiu< : .. 

 The comfortable and wealthy burghers of the great towns re- 

 quired their own portraits and those of their motherly wives t 

 be painted for them heavy and rather coarse-looking heads, 

 rendered with perfect fidelity and very little attempt at flattery 

 by truthful and minutely-accurate artists. Besides these, they 

 liked to see their houses and their tulip-gardens put on canvan 

 for them, the familiar streets of their own clean and bright 

 cities, the peaceful canals and long avenues of their country 

 resorts. They appreciated also the little half-humorous scenes 

 of everyday life, rendered in a style of careful caricature or 

 (grotesque exaggeration an apple-woman in the market-place, 

 a group of boys playing in the street, a rural merry-making, 

 a couple of old tavern cronies sitting over their foaming mugs 

 at the village inn. But beyond such themes their artiste seldom 

 ventured. Dutch art, in fact, is the product of essentially 

 commonplace feeling, and produced for commonplace mind.-, 

 though often elevated by the extremely high character of its 

 technical execution into the very first rank of artistic pro- 

 duction. 



The Flemish painters, Teniers, father and son, may be con- 

 I sidered as a connecting link between the Dutch school and its 

 j southern predecessors. The elder Teniers was an Antwerp 

 man, and studied under Kubens, but his own style was quite 

 Movel, and exhibits strikingly the gradual transformation of art 

 from its older sacred associations to its modern and purely 

 aesthetic purpose. He painted chiefly scenes of low We, such 

 as village fairs and merry-makings, with a profusion of big, 

 jolly, beer-drinking boors and stout Flemish house-wives' 

 carousing and junketing in true careless low Dntch fashion. 

 His humour is inimitable, but it is also mixed up with much 

 gross animalistic coarseness. The younger Teniers for the 

 most part followed his father, but his technique is more finished, 

 and he spent more pains upon his rustic pictures. 



In Holland proper that is to say, in the northern part of the 

 United Provinces a native school of painting had begun to 

 develop itself, at Leyden and elsewhere, from the middle of the 

 fifteenth century, and even at an early period it produced some 

 painters of repute, such as Aartgen. It was not till the be- 

 ginning of the seventeenth century, however, that Dntch art 

 began to reach its culminating point. The greatest name 

 among the Dutch painters is unquestionably that of Rembrandt, 

 who nevertheless has fewer of the characteristic marks of the 

 school than any other. Rembrandt was born at Leyden, the 

 metropolis of art and culture for tho whole of the Netherlands, 

 in 1606. He was a painter, engraver, and etcher ; but he wa 

 entirely home-taught, and his merits and defects are peculiarly 

 his own. He particularly devoted himself to portrait painting, 

 in which he excelled. His treatment of light and shade is 

 unique, and though it shows much mannerism, and is not 

 wholly true to nature as ordinarily seen, it yet marks out his 

 strong individuality of touch. Rembrandt delighted in massive 

 depths of shadow, throwing up the face or other main portions 

 of hi.s work into a high relief of brilliant light. As a rule, his 

 background is rendered in the most sombre and heavy shade, 

 while a powerful beam is cast upon the principal part of the 

 picture. The effect is one of a somewhat lurid but grandiose 

 character, while at the same time the gloom of the whole work 

 often almost oppresses one by its powerful suggestiveneas. 

 Rembrandt's colouring is also peculiarly sober ; he never in- 

 dulges in tbe bright tones of many southern painters, but i 



