var presentation = ["<word>Earliest Arithmetics<\/word>","<phrase>The <strong data-readahead=\"Earliest Arithmetics\">Earliest Arithmetics<\/strong> in English\nby Anonymous<\/phrase>","<word>MATTER<\/word>","<phrase>THE SUBJECT <strong data-readahead=\"MATTER\">MATTER<\/strong>.<\/phrase>","<word>Ancient<\/word>","<word>medieval writers<\/word>","<word>between<\/word>","<word>Art of Arithmetic<\/word>","<word>classical treatises<\/word>","<word>Euclid among the Greeks<\/word>","<word>Boethius among the Latins<\/word>","<word>Science of Arithmetic<\/word>","<word>Astronomy the Art of Calculation<\/word>","<word>considerable progress<\/word>","<word>early treatises<\/word>","<word>long<\/word>","<word>alphabetic notation<\/word>","<word>Specimen<\/word>","<word>Egyptian methods<\/word>","<word>abacus<\/word>","<word>use<\/word>","<phrase><strong data-readahead=\"Ancient\">Ancient<\/strong> and <strong data-readahead=\"medieval writers\">medieval writers<\/strong> observed a distinction <strong data-readahead=\"between\">between<\/strong> the Science\nand the <strong data-readahead=\"Art of Arithmetic\">Art of Arithmetic<\/strong>. The <strong data-readahead=\"classical treatises\">classical treatises<\/strong> on the subject, those\nof <strong data-readahead=\"Euclid among the Greeks\">Euclid among the Greeks<\/strong> and <strong data-readahead=\"Boethius among the Latins\">Boethius among the Latins<\/strong>, are devoted to\nthe <strong data-readahead=\"Science of Arithmetic\">Science of Arithmetic<\/strong>, but it is obvious that coeval with practical\n<strong data-readahead=\"Astronomy the Art of Calculation\">Astronomy the Art of Calculation<\/strong> must have existed and have made\n<strong data-readahead=\"considerable progress\">considerable progress<\/strong>. If <strong data-readahead=\"early treatises\">early treatises<\/strong> on this art existed at all\nthey must, almost of necessity, have been in Greek, which was the\nlanguage of science for the Romans as <strong data-readahead=\"long\">long<\/strong> as Latin civilisation\nexisted. But in their absence it is safe to say that no involved\noperations were or could have been carried out by means of the\n<strong data-readahead=\"alphabetic notation\">alphabetic notation<\/strong> of the Greeks and Romans. <strong data-readahead=\"Specimen\">Specimen<\/strong> sums have indeed\nbeen constructed by moderns which show its possibility, but it is absurd\nto think that men of science, acquainted with <strong data-readahead=\"Egyptian methods\">Egyptian methods<\/strong> and in\npossession of the <strong data-readahead=\"abacus\">abacus<\/strong>,[2*] were unable to devise methods for its <strong data-readahead=\"use\">use<\/strong>.<\/phrase>","<word>INSTRUMENTS USED IN CALCULATION<\/word>","<phrase>THE PRE-MEDIEVAL <strong data-readahead=\"INSTRUMENTS USED IN CALCULATION\">INSTRUMENTS USED IN CALCULATION<\/strong>.<\/phrase>","<phrase>The following are known:--<\/phrase>","<word>polished surface<\/word>","<phrase>(1) A flat <strong data-readahead=\"polished surface\">polished surface<\/strong> or tablets, strewn with sand, on which\nfigures were inscribed with a stylus.<\/phrase>","<word>polished tablet<\/word>","<phrase>(2) A <strong data-readahead=\"polished tablet\">polished tablet<\/strong> divided longitudinally into nine columns (or more)\ngrouped in threes, with which counters were used, either plain or marked\nwith signs denoting the nine numerals, etc.<\/phrase>","<phrase>(3) Tablets or boxes containing nine grooves or wires, in or on which\nran beads.<\/phrase>","<word>horizontal lines<\/word>","<phrase>(4) Tablets on which nine (or more) <strong data-readahead=\"horizontal lines\">horizontal lines<\/strong> were marked, each\nthird being marked off.<\/phrase>","<word>fourth class<\/word>","<word>Salamis<\/word>","<word>chief part<\/word>","<word>parallel lines<\/word>","<word>cross<\/word>","<word>arithmetical symbols<\/word>","<phrase>The only Greek counting board we have is of the <strong data-readahead=\"fourth class\">fourth class<\/strong> and was\ndiscovered at <strong data-readahead=\"Salamis\">Salamis<\/strong>. It was engraved on a block of marble, and\nmeasures 5 feet by 2\u00bd. Its <strong data-readahead=\"chief part\">chief part<\/strong> consists of eleven <strong data-readahead=\"parallel lines\">parallel lines<\/strong>,\nthe 3rd, 6th, and 9th being marked with a <strong data-readahead=\"cross\">cross<\/strong>. Another section\nconsists of five <strong data-readahead=\"parallel lines\">parallel lines<\/strong>, and there are three rows of\n<strong data-readahead=\"arithmetical symbols\">arithmetical symbols<\/strong>. This board could only have been used with counters\n(_calculi_), preferably unmarked, as in our treatise of _Accomptynge by\nCounters_.<\/phrase>","<word>CLASSICAL ROMAN METHODS OF CALCULATION<\/word>","<phrase><strong data-readahead=\"CLASSICAL ROMAN METHODS OF CALCULATION\">CLASSICAL ROMAN METHODS OF CALCULATION<\/strong>.<\/phrase>","<word>Rome<\/word>","<word>first method<\/word>","<word>hand<\/word>","<word>learn<\/word>","<word>Horace<\/word>","<word>Persius<\/word>","<word>abaco numeros<\/word>","<word>scit risisse<\/word>","<word>Apul<\/word>","<word>Apolog<\/word>","<word>Mart<\/word>","<word>Capella<\/word>","<word>Cicero<\/word>","<word>expert calculator<\/word>","<word>Deorum<\/word>","<word>Pallio<\/word>","<word>Adeo<\/word>","<word>est eboris<\/word>","<word>precious metals<\/word>","<word>nigris aureos argenteosque habebat denarios<\/word>","<word>Satyricon<\/word>","<phrase>We have proof of two methods of calculation in <strong data-readahead=\"ancient\">ancient<\/strong> <strong data-readahead=\"Rome\">Rome<\/strong>, one by the\n<strong data-readahead=\"first method\">first method<\/strong>, in which the surface of sand was divided into columns by a\nstylus or the <strong data-readahead=\"hand\">hand<\/strong>. Counters (_calculi_, or _lapilli_), which were kept\nin boxes (_loculi_), were used in calculation, as we <strong data-readahead=\"learn\">learn<\/strong> from <strong data-readahead=\"Horace\">Horace<\/strong>'s\nschoolboys (Sat. 1. vi. 74). For the sand see <strong data-readahead=\"Persius\">Persius<\/strong> I. 131, \"Nec qui\n<strong data-readahead=\"abaco numeros\">abaco numeros<\/strong> et secto in pulvere metas <strong data-readahead=\"scit risisse\">scit risisse<\/strong>,\" <strong data-readahead=\"Apul\">Apul<\/strong>. <strong data-readahead=\"Apolog\">Apolog<\/strong>. 16\n(pulvisculo), <strong data-readahead=\"Mart\">Mart<\/strong>. <strong data-readahead=\"Capella\">Capella<\/strong>, lib. vii. 3, 4, etc. <strong data-readahead=\"Cicero\">Cicero<\/strong> says of an\n<strong data-readahead=\"expert calculator\">expert calculator<\/strong> \"eruditum attigisse pulverem,\" (de nat. <strong data-readahead=\"Deorum\">Deorum<\/strong>,\nii. 18). Tertullian calls a teacher of arithmetic \"primus numerorum\narenarius\" (de <strong data-readahead=\"Pallio\">Pallio<\/strong>, _in fine_). The counters were made of various\nmaterials, ivory principally, \"<strong data-readahead=\"Adeo\">Adeo<\/strong> nulla uncia nobis <strong data-readahead=\"est eboris\">est eboris<\/strong>, etc.\"\n(Juv. XI. 131), sometimes of <strong data-readahead=\"precious metals\">precious metals<\/strong>, \"Pro calculis albis et\n<strong data-readahead=\"nigris aureos argenteosque habebat denarios\">nigris aureos argenteosque habebat denarios<\/strong>\" (Pet. Arb. <strong data-readahead=\"Satyricon\">Satyricon<\/strong>, 33).<\/phrase>","<word>Roman<\/word>","<word>appear<\/word>","<word>third class<\/word>","<word>number<\/word>","<word>transverse wires<\/word>","<word>left hand portion<\/word>","<word>left hand beads<\/word>","<word>right hand<\/word>","<word>Swanpan<\/word>","<word>Far East<\/word>","<word>Russian stchota<\/word>","<word>Eastern Europe<\/word>","<phrase>There are, however, still in existence four <strong data-readahead=\"Roman\">Roman<\/strong> counting boards of a\nkind which does not <strong data-readahead=\"appear\">appear<\/strong> to come into literature. A typical one is of\nthe <strong data-readahead=\"third class\">third class<\/strong>. It consists of a <strong data-readahead=\"number\">number<\/strong> of <strong data-readahead=\"transverse wires\">transverse wires<\/strong>, broken at\nthe middle. On the <strong data-readahead=\"left hand portion\">left hand portion<\/strong> four beads are strung, on the right\none (or two). The <strong data-readahead=\"left hand beads\">left hand beads<\/strong> signify units, the <strong data-readahead=\"right hand\">right hand<\/strong> one five\nunits. Thus any <strong data-readahead=\"number\">number<\/strong> up to nine can be represented. This instrument is\nin all essentials the same as the <strong data-readahead=\"Swanpan\">Swanpan<\/strong> or <strong data-readahead=\"Abacus\">Abacus<\/strong> in <strong data-readahead=\"use\">use<\/strong> throughout\nthe <strong data-readahead=\"Far East\">Far East<\/strong>. The <strong data-readahead=\"Russian stchota\">Russian stchota<\/strong> in <strong data-readahead=\"use\">use<\/strong> throughout <strong data-readahead=\"Eastern Europe\">Eastern Europe<\/strong> is\nsimpler still. The method of using this system is exactly the same as\nthat of _Accomptynge by Counters_, the right-<strong data-readahead=\"hand\">hand<\/strong> five bead replacing\nthe counter <strong data-readahead=\"between\">between<\/strong> the lines.<\/phrase>","<word>BOETHIAN ABACUS<\/word>","<phrase>THE <strong data-readahead=\"BOETHIAN ABACUS\">BOETHIAN ABACUS<\/strong>.<\/phrase>","<word>classical times<\/word>","<word>tenth century<\/word>","<word>fifth century<\/word>","<word>end<\/word>","<word>second class<\/word>","<word>great probability<\/word>","<word>whole passage<\/word>","<word>Boethian<\/word>","<word>return<\/word>","<phrase><strong data-readahead=\"Between\">Between<\/strong> <strong data-readahead=\"classical times\">classical times<\/strong> and the <strong data-readahead=\"tenth century\">tenth century<\/strong> we have little or no\nguidance as to the art of calculation. 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			type:'POST',
			url:'/logging/logPlayerAction.php',
			data: { 'documentId':225,
					'userId':0,
					'playerAction':action,
					'playerArea':area,
					'details':details,
					'timestamp': t
				}
		})
		.done(function(results){
		})
		.fail(function( jqXHR, textStatus ) {
			alert( "Request failed: " + textStatus );
		});

	}