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Library/Paris Manuscript L/52

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Paris Manuscript L — 52

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Bibliothèque de l'Institut de France, Paris

Capovolto.

Semplice1.

Uno spende 1/3 de' sua danari e li rimase 18. Domando quanto avea. Poniamo avessi 12, che spese 4 e li restò 8, e la tema diceva 18. Ora dì pella regola del 3: "Se 8 vien da 12, da che verrà 18?" E così trovi: vien da 27.

Truovami un numero che 5 ne sia li 2/3. Poni un numero a tuo modo e pigliane li 2/3 e vedi se tu hai 5. Se non, dì: "Se questo vien da quel ch'io mi puosi, da che verrà 5?" Verrà da 7 1/2.

"7 di che numero fu e 3/4?" Parti 7 per 3 e quel che ne viene, multiplica per 4, e la somma2 resultata fu il numero di che 7 fu e sua 3/4.

Upside down.

Simple. Someone spends 1/3 of his money and 18 remains to him. I ask how much he had. Let us suppose he had 12, so that he spent 4 and 8 remained; but the problem said 18. Now say by the rule of three: "If 8 comes from 12, from what will 18 come?" And so you find: it comes from 27. Find me a number of which 5 is its 2/3. Set down a number as you please, take its 2/3, and see whether you have 5. If not, say: "If this comes from the one I set down, from what will 5 come?" It will come from 7 1/2. "7 was 3/4 of what number?" Divide 7 by 3 and multiply the result by 4, and the sum obtained was the number of which 7 was its 3/4.

Merchant problems solved by the rule of three

Money spent, and finding a number from its fractional part

Arithmetic & Proportion

A page of worked arithmetic exercises, written upside down. The first is a money problem: someone spends 1/3 of his money and 18 remains, so by a trial value and the rule of three the original sum is found to be 27. Two further problems find a number from a stated fraction of it, giving 7 1/2 for the number whose 2/3 is 5, and applying the divide-then-multiply rule to 7 as 3/4.

On this page

How much money was there before spending a third

Someone spends 1/3 of his money and 18 remains; how much did he have? Leonardo tests the value 12 (spend 4, leaving 8) against the required 18, then by the rule of three 'if 8 comes from 12, from what does 18 come?' finds the answer, 27.

Finding the number from a fraction of it

To find the number whose 2/3 is 5, guess a value, take its 2/3, and adjust by proportion, reaching 7 1/2. The closing case finds the number of which 7 is 3/4 by dividing 7 by 3 and multiplying the result by 4.

Reader's Edition — described with AI from the e-Leo transcription.