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

### From inside the book

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**equilateral**triangle is a triangle which has its three sides equal to one another . Def . XXV . An isosceles triangle is a triangle which has two sides equal . ( An**equilateral**triangle may be regarded as an isosceles triangle if only ... Page 6

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**equilateral**triangle , or to make one line perpendicular to another , without the aid of any sim- pler processes ; that is to say , we might at once imagine any figure to be before us , and then reason about its pro- perties . But part ... Page 13

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**equilateral**A , to reason about , there is nothing to hinder us from con- ceiving the figure at once . The object of the problems is purely that described in the preceding paragraph . Again , it is not the object of the theorems to ... Page 15

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**equilateral**triangle . * The following postulates and axioms are made use of in the construction and demonstration in this proposition : — 1. Postulate I. A straight line may be drawn from a given point to any other given point . 2 ... Page 16

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**equilateral**△ , and is con- structed on the line A B. It would have done equally well if we had taken the point D , and joined D and A , and D and B. The demon- stration would have been word for word the same as above , only ...### 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

### Popular passages

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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