## The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VI |

### From inside the book

Page 154

If two triangles

If two triangles

**have one angle of the one equal to one angle of the other**and the sides about these angles proportional , they are similar , and those angles which are opposite to the homologous sides are equal . Page 157

If two triangles

If two triangles

**have one angle of the one equal to one angle of the other**, and the sides about one other angle in each proportional , so that the sides opposite the equal angles are homologous , the triangles have their third angles ... Page 167

If two triangles

If two triangles

**have one angle of the one equal to one angle of the other**, and a second angle of the one supplementary to a second angle of the other , then the sides about the third angles are proportional . Page 176

If two triangles or parallelograms

If two triangles or parallelograms

**have one angle of the one equal to one angle of the other**, their areas have to one another the ratio compounded of the ratios of the including sides of the first to the including sides of the second .### What people are saying - Write a review

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### Common terms and phrases

ABCD according angle BAC antecedent arc HK base bisected Book called centre chord circle whose centre circles touch circumference coincide common consequent construction Conversely corresponding described diagonal diameter difference distance divided draw drawn duplicate ratio equal equal circles equiangular equilateral externally extremities fall Find fixed four given circle given point given ratio given straight line greater half Hence homologous inscribed internally intersect joining kind less lies line joining magnitudes manner mean meet meet the circumference minor arc multiple parallel parallelogram passes perpendicular polygon Prob produced proportional Prove quadrilateral radii radius ratio ratio compounded rectangle contained rectilineal figure regular respectively right angles sector segment Shew sides similar square standing straight line taken tangent THEOR third triangle ABC whole

### Popular passages

Page 167 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 169 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...

Page 30 - In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.

Page 171 - ... are to one another in the duplicate ratio of their homologous sides.

Page 150 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page 115 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Let...

Page 101 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 96 - ... if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.

Page 150 - When there are any number of magnitudes of the same kind, the first is said to have to the last of them the ratio compounded of the ratio which the first has to the second, and of the ratio whi.ch the second has to the third, and of the ratio which the third has to the fourth, and so on unto the last magnitude. For example, if A, B, C, D be four magnitudes of the same kind, the first...