Propositiones - Part 1 - Answer

I presented the problem for Part 1 here.  The answer is as follows.

The merchant would need to buy 1 boar, 9 sows, and 90 piglets.  As there are three variables and only two equations, trial and error must be employed.  My solution is as follows.

X=Number of Boars
Y=Number of Sows
Z=Number of Piglets

[Eq 1]  X+Y+Z = 100
[Eq 2] 10X+5Y+0.5Z = 100

Solving Equation 1 for Z and substituting into Equation 2 and simplifying you get the following equation.

[Eq3] 1.9X + 0.9Y = 10

This is where trial and error comes in and you get X=1, Y=9.  Back substituting into Equation 1, you get that Z=90.

Hope you had fun!

Propositiones - Part 1

Alcuin of York developed a series of mathematical problems for his students.  Many of these remain and are collected in the document entitled: Propositiones ad acuendos juvenes or Problems to sharpen the young.  This collection contains 56 problems, many of which have similar structure, along with corresponding answers.  These problems are presented by Hadley and Singmaster [1].  I thought it would be fun and educational to post some problems from time to time.  I'll modify them slightly for the audience.

Problem 5: The merchant and 100 dollars
A merchant wanted to buy 100 pigs for 100 dollars.  A boar cost 10 dollars, a sow cost 5 dollars, and a pair of piglets cost a dollar.  How many of each did the merchant buy?

Answer will be posted tomorrow.

[1] Hadley, J. and Singmaster, D. "Problems to Sharpen the Young", The Mathematical Gazette, Vol. 76, No. 475, The Use of the History of Mathematics in the Teaching of Mathematics (Mar., 1992), pp. 102-126

St. Teresa of Avila

Bernini, Ecstacy of St. Teresa, 1647–1652

Let nothing disturb thee;
Let nothing dismay thee:
All thing pass;
God never changes.
Patience attains
All that it strives for.
He who has God
Finds he lacks nothing:
God alone suffices.

Alcuin of York

Alcuin was an eminent educator, scholar, and theologian born about 735; died 19 May, 804. He came of noble Northumbrian parentage, but the place of his birth is a matter of dispute. It was probably in or near York. While still a mere child, he entered the cathedral school founded at that place by Archbishop Egbert. His aptitude, and piety early attracted the attention of Aelbert, master of the school, as well as of the Archbishop, both of whom devoted special attention to his instruction. In company with his master, he made several visits to the continent while a youth, and when, in 767, Aelbert succeeded to the Archbishopric of York, the duty of directing the school naturally devolved upon Alcuin. During the fifteen years that followed, he devoted himself to the work of instruction at York, attracting numerous students and enriching the already valuable library. While returning from Rome in March, 781, he met Charlemagne at Parma, and was induced by that prince, whom he greatly admired, to remove to France and take up residence at the royal court as "Master of the Palace School". The school was kept at Aachen most of the time, but was removed from place to place, according as the royal residence was changed. In 786 he returned to England, in connection, apparently, with important ecclesiastical affairs, and again in 790, on a mission from Charlemagne. Alcuin attended the Synod of Frankfort in 794, and took an important part in the framing of the decrees condemning Adoptionism as well as in the efforts made subsequently to effect the submission of the recalcitrant Spanish prelates. In 796, when past his sixtieth year, being anxious to withdraw from the world, he was appointed by Charlemagne Abbot of St. Martin's at tours. Here, in his declining years, but with undiminished zeal, he set himself to build up a model monastic school, gathering books and drawing students, as before, at Aachen and York, from far and near. He died 19 May, 804. Source

Jerome

St. Jerome Writing, Caravaggio, 1607

Jerome was born about the year 340 A.D.  He went to Rome, probably about 360, where he was baptized, and became interested in ecclesiastical matters. From Rome he went to Trier, famous for its schools, and there began his theological studies. Later he went to Aquileia, and towards 373 he set out on a journey to the East. He settled first in Antioch, where he heard Apollinaris of Laodicea, one of the first exegetes of that time and not yet separated from the Church. From 374-9 Jerome led an ascetical life in the desert of Chalcis, south-west of Antioch. Ordained priest at Antioch, he went to Constantinople (380-81), where a friendship sprang up between him and St. Gregory of Nazianzus. From 382 to August 385 he made another sojourn in Rome, not far from Pope Damasus. When the latter died (11 December, 384) his position became a very difficult one. His harsh criticisms had made him bitter enemies, who tried to ruin him. After a few months he was compelled to leave Rome. By way of Antioch and Alexandria he reached Bethlehem, in 386. He settled there in a monastery near a convent founded by two Roman ladies, Paula and Eustochium, who followed him to Palestine. Henceforth he led a life of asceticism and study. Jerome died in Bethlehem, September 30, 420.
Source

Good Saint Wenceslaus

Wenceslaus was born around 903 A.D.  His parents were Duke Wratislaw, a Christian, and Dragomir, a heathen. He received a good Christian education from his grandmother (St. Ludmilla) and at Budweis. After the death of Wratislaw, Dragomir, acting as regent, opposed Christianity, and Wenceslaus, being urged by the people, took the reins of government. He placed his duchy under the protection of Germany, introduced German priests, and favoured the Latin rite instead of the old Slavic, which had gone into disuse in many places for want of priests. Wenceslaus had taken the vow of virginity and was known for his virtues. The Emperor Otto I conferred on him the regal dignity and title. For religious and national motives, and at the instigation of Dragomir, Wenceslaus was murdered by his brother Boleslaw. The body, hacked to pieces, was buried at the place of murder, but three years later Boleslaw, having repented of his deed, ordered its translation to the Church of St. Vitus in Prague. The gathering of his relics is noted in the calendars on 27 June, their translation on 4 March; his feast is celebrated on 28 September. 

Source

St. Wenceslaus

Wenceslaus is also the subject of the Christmas Carol bearing his name.  Since, stores are already getting ready for Christmas, why not a carol to get us all in the spirit.

Good King Wenceslas looked out

On the feast of Stephen

When the snow lay round about

Deep and crisp and even

Brightly shone the moon that night

Though the frost was cruel

When a poor man came in sight

Gath'ring winter fuel

"Hither, page, and stand by me

If thou know'st it, telling

Yonder peasant, who is he?

Where and what his dwelling?"

"Sire, he lives a good league hence

Underneath the mountain

Right against the forest fence

By Saint Agnes' fountain."

"Bring me flesh and bring me wine

Bring me pine logs hither

Thou and I will see him dine

When we bear him thither."

Page and monarch forth they went

Forth they went together

Through the rude wind's wild lament

And the bitter weather

"Sire, the night is darker now

And the wind blows stronger

Fails my heart, I know not how,

I can go no longer."

"Mark my footsteps, my good page

Tread thou in them boldly

Thou shalt find the winter's rage

Freeze thy blood less coldly."

In his master's steps he trod

Where the snow lay dinted

Heat was in the very sod

Which the Saint had printed

Therefore, Christian men, be sure

Wealth or rank possessing

Ye who now will bless the poor

Shall yourselves find blessing

Our Lady of Sorrows

And Simeon blessed them, and said to Mary his mother: Behold this child is set for the fall, and for the resurrection of many in Israel, and for a sign which shall be contradicted; And thy own soul a sword shall pierce, that, out of many hearts, thoughts may be revealed. Luke 2:34-35