ces from the sun.d and I will move theplace to stand,ALprinciplesphysics.at awhich es.,ururncu meuleval cosmology anFrom ancient times through the days of Copernicus and Tychoy mechamCo,planet'sLA.orbit must be a circle had been unchallenged. Indeed, a circle was accepted as the perfectgeometrical form, and perfection was accepted as the normal state of heavenly affairs. Thatthe real orbits of planets were ellipses was a triumph for the new astronomy and the rightof Western scientists to pursue their investigations independent of theological doctrines.One fundamental question could not yet be answered: What held the planets in theircourses? As we shall see, the vortex theory of Descartes and Newton's theory of universalgravitation were responses to this challenge.of Venice also sent another courier to Rome, whoshould reach Rome in 9 days. And from Rome toVenice is 250 miles. It happened that by the orderof these lords the couriers started their journeys8.1 Problems1. Solve the following problems from the Trevisoat the same time. It is required to find in howArithmetic:many days they will meet.2. From Nicolas Chuquet’s Tripary, 1484: I am owed3240 florins by a debtor who pays me 1 florin the firstday, 2 the second day, 3 the third day, and so on. Inhow many days will the debt be paid off?A man finds a purse with an unknown number of(a)ducats in it. After he spends 1/4, 1/5, and 1/6 ofthe amount, 9 ducats remain. It is required to findout how much money was in the purse.3. From Robert Recorde's The Whetstone of Witte, 1557:A captain marshalls his army in a square formation.When the square is of one size, he has 284 men toomany. But when he rearranges them in a square oneman more on a side than before, he lacks 25 men. HowA hare is 150 paces ahead of a hound whichpursues him. The hare covers 6 paces each timethe hound covers 10. It is required to know how(b)many paces the hound has made when heovertakes the hare.many men does he have?(c)Venice, commanding him that he should reachVenice in 7 days. The most illustrious SignoriaThe Holy Father sent a courier from Rome to4. From Christoph Clavius's Algebra, 1608: If I gave 7lire to each beggar that came to my door, I would have

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Asked Dec 13, 2019
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Number 2

ces from the sun.
d and I will move the
place to stand,
AL
principles
physics.
at a
which es.
,ururncu meuleval cosmology an
From ancient times through the days of Copernicus and Tycho
y mechamCo,
planet's
LA.
orbit must be a circle had been unchallenged. Indeed, a circle was accepted as the perfect
geometrical form, and perfection was accepted as the normal state of heavenly affairs. That
the real orbits of planets were ellipses was a triumph for the new astronomy and the right
of Western scientists to pursue their investigations independent of theological doctrines.
One fundamental question could not yet be answered: What held the planets in their
courses? As we shall see, the vortex theory of Descartes and Newton's theory of universal
gravitation were responses to this challenge.
of Venice also sent another courier to Rome, who
should reach Rome in 9 days. And from Rome to
Venice is 250 miles. It happened that by the order
of these lords the couriers started their journeys
8.1 Problems
1. Solve the following problems from the Treviso
at the same time. It is required to find in how
Arithmetic:
many days they will meet.
2. From Nicolas Chuquet’s Tripary, 1484: I am owed
3240 florins by a debtor who pays me 1 florin the first
day, 2 the second day, 3 the third day, and so on. In
how many days will the debt be paid off?
A man finds a purse with an unknown number of
(a)
ducats in it. After he spends 1/4, 1/5, and 1/6 of
the amount, 9 ducats remain. It is required to find
out how much money was in the purse.
3. From Robert Recorde's The Whetstone of Witte, 1557:
A captain marshalls his army in a square formation.
When the square is of one size, he has 284 men too
many. But when he rearranges them in a square one
man more on a side than before, he lacks 25 men. How
A hare is 150 paces ahead of a hound which
pursues him. The hare covers 6 paces each time
the hound covers 10. It is required to know how
(b)
many paces the hound has made when he
overtakes the hare.
many men does he have?
(c)
Venice, commanding him that he should reach
Venice in 7 days. The most illustrious Signoria
The Holy Father sent a courier from Rome to
4. From Christoph Clavius's Algebra, 1608: If I gave 7
lire to each beggar that came to my door, I would have
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ces from the sun. d and I will move the place to stand, AL principles physics. at a which es. ,ururncu meuleval cosmology an From ancient times through the days of Copernicus and Tycho y mechamCo, planet's LA. orbit must be a circle had been unchallenged. Indeed, a circle was accepted as the perfect geometrical form, and perfection was accepted as the normal state of heavenly affairs. That the real orbits of planets were ellipses was a triumph for the new astronomy and the right of Western scientists to pursue their investigations independent of theological doctrines. One fundamental question could not yet be answered: What held the planets in their courses? As we shall see, the vortex theory of Descartes and Newton's theory of universal gravitation were responses to this challenge. of Venice also sent another courier to Rome, who should reach Rome in 9 days. And from Rome to Venice is 250 miles. It happened that by the order of these lords the couriers started their journeys 8.1 Problems 1. Solve the following problems from the Treviso at the same time. It is required to find in how Arithmetic: many days they will meet. 2. From Nicolas Chuquet’s Tripary, 1484: I am owed 3240 florins by a debtor who pays me 1 florin the first day, 2 the second day, 3 the third day, and so on. In how many days will the debt be paid off? A man finds a purse with an unknown number of (a) ducats in it. After he spends 1/4, 1/5, and 1/6 of the amount, 9 ducats remain. It is required to find out how much money was in the purse. 3. From Robert Recorde's The Whetstone of Witte, 1557: A captain marshalls his army in a square formation. When the square is of one size, he has 284 men too many. But when he rearranges them in a square one man more on a side than before, he lacks 25 men. How A hare is 150 paces ahead of a hound which pursues him. The hare covers 6 paces each time the hound covers 10. It is required to know how (b) many paces the hound has made when he overtakes the hare. many men does he have? (c) Venice, commanding him that he should reach Venice in 7 days. The most illustrious Signoria The Holy Father sent a courier from Rome to 4. From Christoph Clavius's Algebra, 1608: If I gave 7 lire to each beggar that came to my door, I would have

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Expert Answer

Step 1

The sum of n terms of an AP where a is the first term, d is the common difference is given by,

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[2a+(n-1)d] S.

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Step 2

Here, first 1 florin is paid then 2 then 3 and so on.

So, the series formed will be

1,2,3,….

Thus, a=1

Step 3

The series is AP as the term is increasing by 1 (d=1).

The sum of ...

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S, =[2a+ (n-1)d] 3240 = [2(1)+(n-1)(1)] 6480 = n(2+n-1) 6480 = n(n+1) n +n-6480 = 0 n +81n – 80n– 6480 = 0 n(n+81)– 80(n+81) = 0 (n-80)(n+81) =0 n= 80, –81

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