## The first and second books of Euclid explained to beginners, by C.P. Mason1872 - Geometry |

### From inside the book

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**less**than a right angle . Def . XV . A circle is a plane bounded figure , con- tained by one line , which is called the circumference , and is such , that every point in it is at the same dis- tance from a certain point within , which ... Page 7

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**less**to the**less**, the sum of the two larger magnitudes will be larger than the sum of the two**less**. * The process by which any figure is produced , is called the construction of the figure . VI . Things which are doubles of the same ... Page 8

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**less**than two right angles , those lines will meet if produced . C. If part of one bounded figure ( and part only ) be inside another bounded figure , the peripheries of those * This is properly only a particular case of the second ... Page 20

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**less**. To do this we must be able , - 1. From a given point to draw a straight line equal to a given straight line . ( Prop . II . ) 2. With a given centre , and at a given distance from that centre , to describe a circle . ( Post . III ... Page 29

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**less**than B , A is greater than B ( A and B being two magnitudes that admit of comparison ) , it is clear that one or other must be true . If we can show that A is not equal to B , and also that A is not**less**than B , it follows that ...### Other editions - View all

The First and Second Books of Euclid Explained to Beginners, by C.P. Mason Euclides No preview available - 2016 |

### Common terms and phrases

A B and CD A B is equal A C and CB Æneid axiom beginner bisected centre Consequently diagonal draw a straight Edition equal in area equal respectively equal to twice equilateral Euclid exterior exterior angle Fcap figure finite right line follows formed given finite right given line given point given rectilineal given straight line gnomon greater half a right hypotenuse interior and opposite isosceles Join the points join two given Jugurtha Latin length less line A B line CD linear units lines are parallel magnitudes meeting the line opposite sides parallelogram point F proof Prop proposition prove this proposition rectangle contained right angles side A C straight line meets suppose three sides triangle unequal

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Page 13 - CARPENTER'S (Dr. WB) Zoology. A Systematic View of the Structure, Habits, Instincts, and Uses of the principal Families of the Animal Kingdom, and of the chief Forms of Fossil Remains. Revised by WS Dallas, FLS Numerous Woodcuts. 2 vols. 6s. each. — Mechanical Philosophy, Astronomy, and Horology. A Popular Exposition. 181 Woodcuts. CARPENTER'S Works.— Continued. — Vegetable Physiology and Systematic Botany.

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Page 144 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Page 149 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC...

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Page 152 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Page 12 - Social advancement is as completely under the control of natural law as is bodily growth. The life of an individual is a miniature of the life of a nation.

Page 6 - The Enunciations and Figures belonging to the Propositions in the First Six and part of the Eleventh Books of Euclid's Elements, (usually read in the Universities,) prepared for Students in Geometry. By the Rev. J. Brasse, DD New Edition. Fcap. 8vo. Is. On cards, iu case, 5s.

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