ALT 



the ftudy of the oriental languajres, he puthimfelf, in i6i^> 

 under the tuition of a Jcv.i:h Kabbi, at Enibden. Upon 

 his vilit to England, in '.6^0, he was admitted to clerical 

 oi-ders bv Dr. Prideaux, bifhop of Woiceiler ; but he al- 

 tered his purpofe of continued refidence in this country, as 

 foon as lie received an invitation to the Hebrew prnfcflbrflup, 

 at Groningen. He returned to Germany in 1643, and ob- 

 tained confiderable diftindions of honour in the univerfity. 

 In this fituation a rivalAiip commenced between him and his 

 colleague, in the piofefTorfliip of divinity, Des Marets. 

 The fatter was addifted to the fcholaftic pliilofophy and 

 plan of inrtruclion ; whereas the former devoted himfelf to 

 the ftudy of the Scriptures and Rabbinical learning, and 

 acquired a degree of popularity, as a kdurer, which excited 

 the jealoufy and oppofition of Des Marets and his adherents. 

 A difi'/Ute between thefe coadjutors, who were now become 

 competitors and rivals, had for fome time prevailed ; and at 

 length the dccifion of it was referred to the divines of 

 Levden. Thefe umpires pronounced Alting innocent of 

 her'efy, but fond of innovation, and Des Marets deficient in 

 nicdelly and candour. The civil power was at laft obliged 

 to interfere, and the penalty of deprivation was decreed 

 aga'nft thofe divines, who fhould in any ecclefiaftical aflembly 

 revive the Marefio-Altingian controvcrfy. The n-.agillrates 

 proceeded by an ufurpation of authority which did net 

 belong to them, to prohibit even writing for or againft t!;^ 

 judgment of the divines of Leydcn. This breach between 

 the two profeffors was never thoroughly compromifed ; 

 though, by the inte^-pofition of friends, a kind of formal re- 

 conciliation was effedled, while Des Marets lay on his death- 

 bed. Alting did not long furvive him, but v^as taken off 

 by a fever, in 1679. He was reproached, in confequence 

 of his attachment to Rabbinical learning, with an inclination 

 to become a Jew. His works were collefted fome years 

 after his death, and pubhdied in five volumes foho, under 

 -tiie care of Bekker, miniiler at Amfterdam, bj- his coufin 

 Menfo Alting, burgo-mailer of Groningen, who wrote a 

 good defcription of the Low Coimtries, entitled, " Notitia 

 GcrnianioE Inferioris." It is faid that he preached well in 

 three languages, German, Dutch, and Englifh. Gen. 

 Dia. 



ALTITUDE, in Geometry, the third dimenfon of body, 

 confidered with regard to its elevation above the ground — 

 called alfo height or depth. 



Altitude of a figure, is the diftance of its vertex from 

 its bafe, or the , length of a perpendicular let fall from the 

 vertex t<J the bafe. 



Thus, K L [PLite I. Geometry, fjr. 2.) being taken for the 

 bafe of the right angled-triangle, KLM : the perpendicular 

 KM will be the altitude of the triangle. 



Triangles of equal bafes and altitudes are eq\:al ; and pa- 

 rallelograms, whole bafes and altitudes are equal to thofe of 

 triangles, are juft the double thereof. 



Altitude, in Optics, is ufually confidered as the angle 

 fubtended between a line drawn through the eye, parallel to 

 the horizon, and a vifual ray emitted from an objefl to the 

 «ye. 



For the laws of the vifion of altitudes. See Vision. 



If through the two extremes of an objeft, S and T {Plate 

 I. OptL-!, _fy. 13.) two parallels, TV and SQ_j5e drawn ; 

 the angle TVS, intercepted between a ray palling through 

 the vertex. S, and terminating the (liadow thereof in V, 

 makes, with the right line TV, what is called, by fome 

 writers, tlie Jtlt'itude of the Luminary. 



Altitude, in Ccfmo^riiphy, is the perpendicular height 

 of an objeft, above the plane of the horizon. 



1 



ALT 



/Ihituclts are divided into aceeffibk and inac:eJsH!. 



Altitude, aceeffille, of an objed, is that whofe bafe 

 you can have acccfs to, fo as to meafure the nearetl dillance 

 between your ilation, and the foot of the objeft on the 

 ground. 



Altitude, inaccefflUc, of an cbjeft, is that whofe bafe 

 cannot be approached, by reafon of fom.e impediment ; fuch 

 as water, or the like. 



There are three ways of meafuring altitudes, i-ix. gecme- 

 triccdly, trigonometric ally, and optically. — The firft is fome"- 

 what indireft and unartful ; the fecond is performed by 

 means of inihumcnts for the purpofe ; and tlie third by 

 (hadows. 



The inftruments chiefly ufcd in mcnfuring of altitudes, 

 are the quadrant, theodolite, geometric quadrat, or line of 

 {hadows, &c. the defcriptions, applications, &c. whereof, 

 lee under their refpective articles Quadrant, Theodo- 

 lite, and Qliadrat. 



Altitudes, to tale accejftlle. To meafure an acceflible 

 altitude geometrically. — Suppofe it required to find the alti- 

 tude AB {Plate I. Geometry, fg. 3.) plant a llaff, DE, 

 perpendicularly in the ground, of fuch height as may be 

 equal to the height of the eye. Then, lying prollrate on the 

 ground, with your feet to the ftaff ; if E and B prove in 

 the fame right line with the eye C, the length C A is equal 

 to the altitude AB. If fome other lower point, as F, 

 prove in the hne with E, and the eye, you mud remove the 

 llafT, &c. nearer to the obje£l ; on the contrary, if the line 

 continued from the eye over E, mark out fome point above 

 the altitude required ; the ftaff, &c. are to be removed 

 farther off, till the line CE raife the very point required. — 

 Thus, meafuring the dillanee of the eye C from the foot of 

 the objeft A, the altitude is had ; fince CA=AB. 



Or thus : at the diilance of thirty, foity, or more feet, 

 plant a ftaff DE {fg. 4.) and at a diftance from this, in 

 C, plant another fhorter one, fo as that the eye being ui F, 

 E and B may be in the fame right line therewith. Meafure 

 the diftance between the two ftaves, GF; and between 

 the fliorteft ftaff and the objeft, HF ; as alfo, the differ- 

 ence of the heights of the ifaves, GE.— To GF, GE, 

 and H F, find a fourth proportional BH. — To this add the 

 altitude of the fhorter ftaff, FC. The fum is the altitude 

 required, AB. 



To meafure an accefUble altitude, trigonometrically — 

 Suppofe it required to find the altitude AB {fg. 5.) 

 choofe a ftation in E ; and with a quadrant, theodolite, or 

 other graduated inftrument duly placed, find the quantity 

 of the angle of altitude ADC. Meafure the Ihorteft dif- 

 tance of the ftation from the object, viz. DC, and this of 

 conlequence is perpendicular to AC. 



Now, C being a right angle, it is eafy to find the fide 

 AC ; fince, in the triangle A CD, we have two angles, 

 •uiz. D and A its complement, and a fide oppofite to one of 

 them, CD, the fide oppofite to the other may be eafily 

 found by this canon. As the fine of the angle A is to the 

 given fide oppofite to it D C, fo is the fine of the other angle 

 D to the fide required CA. To this fide, thus found, 

 adding BC, the fum is the perpendicular altitude re- 

 quired. 



Or fay, as radius is to the diftance DC, fo is the tangent 

 of the angle ADC to AC, the height of the objeft ; and 

 adding the altitude of the inftrument above the ground, the 

 whole height of the objeft is found. The operation is 

 beft performed by logarithms. E. G. Suppofe the angle 

 ADC = 51° 52', and the diftance DC = 64 feet. Then 

 it will be, 



Radius 



