## SYLLABUS OF PLANE GEOMETRY |

### Inni boken

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Side 12

If two triangles have two angles of the one equal to two angles of the other , each to each , and have likewise the arms common to these angles equal , * Throughout this Syllabus a method of

If two triangles have two angles of the one equal to two angles of the other , each to each , and have likewise the arms common to these angles equal , * Throughout this Syllabus a method of

**proof**has been indicated wherever it was felt ... Side 13

... one equal to the three sides of the other , each to each , then the triangles are identically equal , and of the angles those are equal which are opposite to equal sides . 14 A SYLLABUS OF [ Alternative

... one equal to the three sides of the other , each to each , then the triangles are identically equal , and of the angles those are equal which are opposite to equal sides . 14 A SYLLABUS OF [ Alternative

**proofs**, ( i PLANE GEOMETRY . Side 14

14 A SYLLABUS OF [ Alternative

14 A SYLLABUS OF [ Alternative

**proofs**, ( i ) by Theors . 14 and 5. ( ii ) By Theors . 6 and 5. ] THEOR . 16. If two triangles have two sides of the one equal to two sides of the other , each to each , but the bases unequal , then the ... Side 24

[ Alternative

[ Alternative

**proofs**:( 1 ) Euclid's . ( 2 ) By dividing two squares placed side by side into parts , which may be combined so as to form a single square ] THEOR . 10. In an obtuse - angled triangle the square on the side opposite the ... Side 32

[ Euclid's

[ Euclid's

**proof**. ] THEOR . 20. Two tangents and two only can be drawn to a circle from an external point . [ By Theor . 15 and Theor . 14 , Cor . ] Cor . The two tangents drawn to a circle from an external point are equal , and make ...### Hva folk mener - Skriv en omtale

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Syllabus of Plane Geometry: (Corresponding to Euclid, Books I - VI ... Uten tilgangsbegrensning - 1876 |

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according altitude angles are equal angles equal antecedent arcs base bisects Book called centre chord circumference circumscribe common conjugate consequent construct corresponding Definitions denoted describe diameter difference distance divided draw equal angles equal circles externally extremes formed former four GEOMETRY given angle given circle given point given ratio given straight line greater angle Hence identically equal inscribed intercepts interior angles internally intersection kind less Limits Loci locus magnitudes major mean meet minor arcs multiple opposite opposite angles pair parallel parallelogram passes perpendicular point of contact polygon position PROB produced proof proportional proposition quadrilateral radii radius ratio compounded rectangle contained rectilineal figure regular respectively right angles Rule of Conversion sectors segment sides similar square stand straight line drawn subtended Superposition SYLLABUS taken tangent THEOR Theorem third three given touch triangle true unequal vertex whence whole wholly

### Populære avsnitt

Side 14 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 17 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...

Side 14 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.

Side 13 - Any two sides of a triangle are together greater than the third side.

Side 23 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 13 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Side 34 - If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally.

Side 56 - If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals.

Side 28 - In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs.

Side 4 - The enunciation of a Theorem consists of two parts, — the hypothesis, or that which is assumed, and the conclusion, or that which is asserted to follow therefrom. Thus in the typical Theorem, If A is B, then C is D, (i), the hypothesis is that A is B, and the conclusion, that C is D.