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many cubic feet are contained in a log of wood, the breadth of the end being 2 feet, and the length 15 feet? 15 x 2 x 260 cubic feet. How many cubic feet and yards of earth will be dug out of a ditch 4 feet broad at the top, 1 foot at the bottom, and 5 feet deep, the length being 1200 feet? As in this question the breadth at top is 4 feet, and at the bottom only 1, the mean breadth is 24. 1200 × 5 × 2 = 9000 feet 9000 =3334 yards. Divide 70 into 2 parts which 27
shall be to one another as 2 to 3.
Divide 100 into 3 parts which shall be to each other as 2, 3, 5.
10 100 2:20
The diameter of a circular fish pond is 12 feet, required the diameter of another whose area shall be nine times that of the other. Extract the square root of 9 = 3 and X 12 = 36. If a solid inch of metal weighs 8 ounces avoirdupois, what is its specific gravity? 8 × 1728 =13824 specific gravity. If a man standing at the side of a river hears his voice reflected from the opposite bank in 3 seconds of time, what is the breadth of the river? 1142 × 14 1713 feet, the breadth of the river. How far will a body descend from a state of rest in 20 seconds? 12: 202:: 16: 64334 feet descends.
RISE AND PROGRESS OF SCIENCE.
How is Science generally defined? Science in its most comprehensive sense only means knowledge, and in its ordinary sense means knowledge reduced to a system; that is, arranged in a regular order so as to be conveniently taught, easily remembered, and readily applied. Where did science first dawn? In the genial climes of the East. What particular spot of the globe was first famed for science? Greece. Who transplanted into Greece the science of the Egyptian priests? Thales, the founder of the Ionic sect. Who first received the name of philosopher or lover of wisdom? Pythagoras, who was born in the island of Samos. Did he recommend his pupils to study? He urged the study of mathematics, and he founded the theory of music, which he cultivated both as an art and a science. Who was the most distinguished of the successors of Pythagoras? Empedocles, who conceived all bodies to consist of infinitely small particles in a state of perpetual motion, held together by the inherent force of matter, yet kept separate by the antagonism of its action. What distinguished philosopher arose after learning and philosophical sects had multiplied over Greece? Socrates arose to give a more useful impulsion to the human mind. What did he think the first step to real knowledge? It was to perceive the extent of our ignorance. What was his great aim as a teacher of philosophy? His grand object was to diffuse solid instruction among the body of Athenian youth. Who was the most illustrious of all the disciples of Socrates? Plato. After having gleaned all the information he could reach in foreign countries he returned home, and purchased
the Grove of Academus at Athens, where he taught youths of the first distinction, who were attracted by the fame of his sublime genius. Was the philosophy of Plato imbued with mysticism? Yes; but to him we are indebted for the beautiful method of geometrical analysis and conic sections. Who was the next distinguished philosopher? Aristotle, who was born at Stagira three hundred and eighty-five years before the Christian æra. How long did he study under the direction of Plato? Twenty years. What did Philip of Macedon request Aristotle to do? To superintend the education of his son Alexander. What did Aristotle do after he educated Alexander? He opened the Peripatetic school at a place called the Lyceum. Did Alexander ever forget Aristotle? No; he held a correspondence with him as long as he lived. What happened to the numerous writings of Aristotle? They were suffered to rot in a damp cellar for a hundred y years after his death, and were never esteemed by the Greek and Roman authors. He was however a distinguished philosopher, the founder of comparative anatomy; his Natural History and Meteorology were wonderful productions. Where did Ptolemy live, the successor of Alexander? In Egypt and in the city of Alexandria, which he made a distinguished seat of learning. He erected a magnificent edifice which he called the Museum, in which men of science were entertained at the public expense, and furnished with books and instruments for the prosecution of their studies. What were the names of the mathematicians who threw a lustre on the first three centuries of the Alexandrian school? Euclid digested the elements of geometry into a system. Apollonius extended the conic sections and improved geometrical analysis. Pappus and Nicomedes invented
some of the higher curves. Who had the merit of fitting out the first voyage of discovery? The republic of Marseilles, a Grecian colony, settled in the south of France. Who sailed first towards the equator? Euthymenes. Who first sailed towards the north pole? Pythias, an able astronomer, first discovered Thule, and remarked the features of the circumpolar climate, and noticed the phænomena of the tides. What nation had the honour of giving birth to Archimedes? Sicily. What kind of philosopher was Archimedes considered to be? The most inventive genius of all antiquity. He deserves to be regarded as the first who really studied natural philosophy on right principles. He discovered the fundamental principle of mechanics and hydrostatics. He pointed out the centre of gravity, unfolded the properties of floating bodies, and traced the rudiments of naval architecture. He made engines to resist for three years the whole efforts of a Roman squadron and besieging army. What happened to Archimedes in the latter part of his life? A soldier entered the apartment of Archimedes and massacred him on the spot, in the seventy-fifth year of his age, and two hundred and twelve before Christ. Who first extended the science of Astronomy? Hipparchus, a genius of a very high order. He found the exact length of the year, ascertained the distance of the moon and approximated to that of the sun, and he distinguished the unequal intervals between the equinoxes. He defined the places on our globe by their latitude and longitude. Who first composed a general treatise of geography, and applied the theory of projections to the construction of maps? Ptolemy, who resided at Alexandria. The study of spherical trigonometry was begun by Hipparchus, extended by Theodosius and
Menelaus, but reduced to a practical form by Ptolemy. Who made improvements in mechanics? Ctesebius improved the clepsydra, invented the pump, and constructed an engine for discharging arrows by means of condensed air. What improvements in science did Hero make? He formed the crane, and contrived machines which acted from the variable elasticity of included air, as affected by heat and cold. What did this principle lead Galileo and Sanctorio afterwards to invent? The construction of our thermometers. Who succeeded the Greeks in political power? The Romans then became masters of the world. Did the Romans make any advancements in science? No; all the knowledge attained by them in arts or philosophy they borrowed immediately from the Greeks. Their education served only to form orators and statesmen. What other race of men became lords of the creation at this time? The Arabians impelled by the enthusiasm of a new religion spread the terror of their arms in all directions. They subdued Egypt, Syria, and Persia, and much of the Eastern empire. In the west they occupied Spain and a great part of France. Did the Arabians esteem the science of the Greeks? Yes; they were passionately fond of the philosophy of the Greeks. What branches of science did they cultivate? They cultivated Geometry, Astronomy, and studied Botany and Chemistry. What was the greatest benefit they rendered to mankind? The communication of the decimal notation of numbers. The use of the ten digits in arithmetic passed over to the Moorish kingdom of Spain, and was transferred to the nations of Europe about the beginning of the fourteenth century, but was not generally adopted till near two hundred years afterwards. What arts did the Arabians practise at that period? They practised brewing