LKSSONS ix <;I:KKK. 



205 



40, 41, 45, and some other*. We trust, after all that haa been 

 said upon tho method of drawing an object with tho use of one 



VP, tin- pupil will have no dillicull y in first drawing the per- 

 apeotive of tho block. Tho principal diiiiculty will ho with the 

 uroh, to draw whioh wo shall have to repeat tho same principles 

 which were employed for the circle on the board (Problem X \ , 

 Fig. 40, page 140) ; therefore, in order to get tho necessary point* 

 throui'h wliii-h the arch ia to be drawn by hand, wo moat rabat 

 the semicircle. From c as a centre draw tho arc / h g ; draw 

 .//it- parallel to / g, and the semi-diagonals c d and c e 

 through the points where these last lines intersect the arc .- 

 draw linos parallel to f d to meet the front of the plan of the 

 building in i and k; visual rays must bo drawn from g, k, c, v,f. 

 From the spring of the arch marked on the line of contact at m, 

 make m n equal to / d ; the visual ray from c the centre will 

 produce the points o and p ; draw the semi-diagonals p r and 

 p s; where those lost lines intersect the visual rays from i and 

 k, will give the points through which the arch ton must be 

 drawn by hand. We have not entered into the other part 

 of the work, as wo have no doubt that our pupils will be able 

 to do it from the experience they have gained in the solution 

 of previous problems. 



PROBLEM XXVI. (Fig. 48). Give a perspective view of a 

 door-frame, a six-panelled door, partly open, tlie door-frame being 

 parallel to the plane of the picture, and the line of sight two-thirds 

 of the height of the door. (From the Military Examination 

 Papers.) 



Thoro are very few conditions given. The door is said to be 

 partly open, therefore it may be placed at any angle at pleasure ; 

 the wall and door-frame may be placed at any distance from 

 the PP, but they must be parallel to the PP ; the proportions of 

 the door and frame are discretionary. This is one of those 

 problems which are frequently given at public examinations 

 with very few working conditions. It gives us an opportunity 

 for advising all who may at any time have to compete in these 

 examinations to use some definite scale in the construction ; it 

 will probably save a great deal of confusion and much un- 

 certainty. There will be much in the drawing of this subject 

 that has occurred before, all of which we shall pass over to 

 avoid unnecessary repetition of former instructions. In the 

 plan it must be observed that the width of the door a b 

 must be made equal to a c tho space within the frame. The 

 division of a b for the plans of the stiles and panels must be 

 proportionally divided, and those proportions must be set off 

 on o d. (See Lessons in Geometry, Problem XVI., Vol. I., 

 page 209.) There are three lines of contact , the first is from 

 a b produced to the PP. Upon this line of contact all the 

 perpendicular measurements of the stiles and panels are 

 arranged. The second line of contact is from the back of the 

 door produced to the PP. This is for the purpose of arriving 

 at the pei-spective thickness of the door ; therefore from the 

 bases of these two lines of contact at e retiring lines are drawn 

 to the VP ; these retiring lines cutting visual rays drawn from 

 the end of the door a in the plan, will give the perspective 

 thickness of the door. The principal retiring lines are those of 

 the top and bottom of the door, and the horizontal edges of 

 the panels, all drawn from tho perpendicular measurements 

 above stated. The third line of contact is g h ; f g being 

 ruade parallel to a 6 for the sake of the advantage of the same 

 VP ; a line drawn from the base of g h towards the VP, cutting 

 a VR from /, gives the position of the base of the frame i k. 

 The width of the frame across the top is obtained thus : 

 n o being the height of the opening of the door, a line must 

 be drawn from n to m at an angle of 135 with n o ; con- 

 sequently, after m r is drawn, m n will be found to bisect the 

 right angler mi; therefore, the visual rays from the plan of 

 the frame at c cutting the line m n will produce tho points in 

 m n from which to draw the mouldings both horizontally and 

 perpendicularly ; PS will be the VP for the interior edge of the 

 frame, as shown in the line drawn from o. The great advan- 

 tage of using several lines of contact will be seen when 

 working the details. We allude to this for the purpose of 

 observing that it is advisable to draw these lines of contact 

 from produced lines of the plan all parallel with each other, 

 so that one vanishing point may be used for all ; otherwise, if 

 they are not parallel, other vanishing points will have to be 

 found, because every retiring line must have its own vanishing 

 point. 



LESSONS IN GREEK. XVIIL 



ADVERBS AND TUEIB FORMATION. 



UNDER the name of adverb* we indicate tfaoM indeclinable 

 words whioh denote the relation* of time and place, or the 

 relations of way and manner; aa *, there ; wv, now; aAr, 



Adverbs of manner are formed from adjective*, by <Tfaiy 

 ui to the pure atom of the adjective. As a practical rule, 700 

 may take this 



The termination -vv of the Genitive Plural of the Adjective it 

 changed into ut ; for example : 



Adjective. Genitive Plural. Adverb. 



<t>t\os, loving, <f>i\<tit>, (f>i\ui, lovingly. 



KoAor, beautiful, na\u>v, KoAus, beautifully 



airAof'f, simple, airKuv, air\u>t, simply. 



iras, all, iravruv, iramtas, altogether. 



(Tutppui/, wise, irwtypovwif, fftixppovuH, wiaely. 



TOXUJ, swift, -raxfwv, raxi, swiftly. 



M7, great, fj.fya\ui', nfya\us, greatly. 



a\7j07)s, true, aKyOtav, aArj&us, truly. 



vyOijs, accustomed, ffvvrjQwv, trumjOut, according to 



custom. 

 The terminations -6n> , -Oi, and -8t form adverbs by being added 



to nouns, pronouns, and verbs, to signify relations of place ; thna 



6( denotes from a place (whence) ; $i, at a place (where) ; and 8 , 

 to a place (whither) -. for example, ovpavodti>,from heaven; ovpavoOi, 

 in heaven ; ovpavovof, to heaven. With pronouns 5t becomes at t 

 thus a\\off(, to some other place ; so with tuti, there, as ncutrt, 

 thither. In the plural of the substantives in -at, -o-8 passes 

 into -e, as Aflijj/o^E for AOyvcurSf , from A9i)vcu, -<av, the city 

 Athens. 



Adverbs of place terminate in -, as avu, above ; Ka.ru, below ; 

 o>, without ; fffw, within. There are many adverbs which are 

 obviously cases of nouns or pronouns, as (airtv7;i (so in Latin, 

 derepente), suddenly; irov, somewhere; &TTOV, ov, wfiere; avrov, 

 on the spot, exactly here or exactly there ; ovtiafnov, nowhere : these 

 adverbs are all genitives. 



Accusatives are also common, as itpwiiv, at the dawn ; poKpav, 

 a long way ; trtpav, beyond a place, whence the country along 

 the east side of the Jordan had the name of Peraea, that is, the 

 land beyond ; Swptav, gratis, gratuitously ; ffi\n.tpov, to~day (Lat. 

 hodie) ; avpwi to-morrow (Lat. eras). 



COMPARISON OF ADVERBS. 



Adverbs of manner have commonly no peculiar adverbial 

 termination, but employ in the comparative the neuter singular, 

 and in the superlative the neuter plural, of the corresponding 

 adjectives. The same fact may be stated thus, namely, that 

 the neuter singular of comparatives may be used adverbially, 

 that is, with an adverbial signification ; and that the neuter 

 plural of superlatives may be used with an adverbial signification, 

 for example : 



From Comparative. Superlative. 



(ffo<pos), wisely, aoqxartpov, <ro^xarara. 



(<ra(pi}s), clearly, acuptompov, ffatfxyrara. 



Xapifvrus (xapttis), charmingly, x"-P l( ^^ f pov, x a P l<rraTa - 

 (v$aifj.ov(es (fvSaifj.<av), happily, fvoai/j.ovf<rr(poy, fvSaiuofttrrara. 

 atffxfxas (a <rxpos), shamefully, ai^x^ov, aurxttrTo. 



f)Sf<as (7j8us), pleasantly, ijSioy, jjSitrra. 



raxftas (raxvs), swiftly, Oarroy, Taxrra. 



Adverbs of place in -o> retain that termination in the com- 

 parative and superlative. 



Comparah't*. Superlative. 



avai, above, avta-rtpta, avu-Tarts. 



KOTO), below, Karui-Tfpoi, Karto-Tarw. 



The comparative and superlative of moat other adverbs of 

 place end in -w, as 



Comparative. Sujvrlah'er. 



iff pa, beyond, ircpatTcpw, (none). 



TT)\OU, at a distance, T^Kortpw, rrj \orarta. 



fKas, at a distance, fKacrrtpa, (Kcurraru. 



ryyvs, near, cyyintpe:, tyjvrttrtt. 



Some adverbs have a reciprocal relation to each other. The 

 simple forms stand as relatives. By prefixing T to the relatives, 



