Question: How did Mendeleec's periodic table predict the properties of elements that hadn't been found yet?
About the article "Periodic table", section "Mendeleev's table".

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The periodic table is a tabular arrangement of the chemical elements, organized on the basis of their atomic numbers, electron configurations (electron shell model), and recurring chemical properties.
Elements are presented in order of increasing atomic number (the number of protons in the nucleus).
The standard form of the table consists of a grid of elements laid out in 18 columns and 7 rows, with a double row of elements below that.
The table can also be deconstructed into four rectangular blocks: the s-block to the left, the p-block to the right, the d-block in the middle, and the f-block below that.
The rows of the table are called periods; the columns are called groups, with some of these having names such as halogens or noble gases.
Since, by definition, a periodic table incorporates recurring trends, any such table can be used to derive relationships between the properties of the elements and predict the properties of new, yet to be discovered or synthesized, elements.
As a result, a periodic table—whether in the standard form or some other variant—provides a useful framework for analyzing chemical behavior, and such tables are widely used in chemistry and other sciences.
Although precursors exist, Dmitri Mendeleev is generally credited with the publication, in 1869, of the first widely recognized periodic table.
He developed his table to illustrate periodic trends in the properties of the then-known elements.
Mendeleev also predicted some properties of then-unknown elements that would be expected to fill gaps in this table.
Most of his predictions were proved correct when the elements in question were subsequently discovered.
Mendeleev's periodic table has since been expanded and refined with the discovery or synthesis of further new elements and the development of new theoretical models to explain chemical behavior.
All elements from atomic numbers 1 (hydrogen) to 118 (ununoctium) have been discovered or reportedly synthesized, with elements 113, 115, 117, and 118 having yet to be confirmed.
The first 98 elements exist naturally although some are found only in trace amounts and were initially discovered by synthesis in laboratories.
Elements with atomic numbers from 99 to 118 have only been synthesized, or claimed to be so, in laboratories.
Production of elements having higher atomic numbers is being pursued, with the question of how the periodic table may need to be modified to accommodate any such additions being a matter of ongoing debate.
Numerous synthetic radionuclides of naturally occurring elements have also been produced in laboratories. 
Russian chemistry professor Dmitri Mendeleev and German chemist Julius Lothar Meyer independently published their periodic tables in 1869 and 1870, respectively.
Mendeleev's table was his first published version; that of Meyer was an expanded version of his (Meyer's) table of 1864.
They both constructed their tables by listing the elements in rows or columns in order of atomic weight and starting a new row or column when the characteristics of the elements began to repeat.
The recognition and acceptance afforded to Mendeleev's table came from two decisions he made.
The first was to leave gaps in the table when it seemed that the corresponding element had not yet been discovered.
Mendeleev was not the first chemist to do so, but he was the first to be recognized as using the trends in his periodic table to predict the properties of those missing elements, such as gallium and germanium.
The second decision was to occasionally ignore the order suggested by the atomic weights and switch adjacent elements, such as tellurium and iodine, to better classify them into chemical families.
With the development of theories of atomic structure, it became apparent that Mendeleev had unintentionally listed the elements in order of increasing atomic number or nuclear charge.
The significance of atomic numbers to the organization of the periodic table was not appreciated until the existence and properties of protons and neutrons became understood.
Mendeleev's periodic tables used atomic weight instead of atomic number to organize the elements, information determinable to fair precision in his time.
Atomic weight worked well enough in most cases to (as noted) give a presentation that was able to predict the properties of missing elements more accurately than any other method then known.
Substitution of atomic numbers, once understood, gave a definitive, integer-based sequence for the elements, still used today even as new synthetic elements are being produced and studied.
Dmitri Ivanovich Mendeleev (; 8 February 1834 – 2 February 1907 O.S.
27 January 1834 – 20 January 1907) was a Russian chemist and inventor.
He formulated the Periodic Law, created his own version of the periodic table of elements, and used it to correct the properties of some already discovered elements and also to predict the properties of elements yet to be discovered. 
An important breakthrough in making sense of the list of known chemical elements (as well as in understanding the internal structure of atoms) was Dmitri Mendeleev's development of the first modern periodic table, or the periodic classification of the elements.
Mendeleev, a Russian chemist, felt that there was some type of order to the elements and he spent more than thirteen years of his life collecting data and assembling the concept, initially with the idea of resolving some of the disorder in the field for his students.
Mendeleev found that, when all the known chemical elements were arranged in order of increasing atomic weight, the resulting table displayed a recurring pattern, or periodicity, of properties within groups of elements.
Mendeleev's law allowed him to build up a systematic periodic table of all the 66 elements then known based on atomic mass, which he published in "Principles of Chemistry" in 1869.
His first Periodic Table was compiled on the basis of arranging the elements in ascending order of atomic weight and grouping them by similarity of properties.
Mendeleev had such faith in the validity of the periodic law that he proposed changes to the generally accepted values for the atomic weight of a few elements and, in his version of the periodic table of 1871, predicted the locations within the table of unknown elements together with their properties.
He even predicted the likely properties of three yet-to-be-discovered elements, which he called ekaboron (Eb), ekaaluminium (Ea), and ekasilicon (Es), which proved to be good predictors of the properties of scandium, gallium, and germanium, respectively, which each fill the spot in the periodic table assigned by Mendeleev.
At first the periodic system did not raise interest among chemists.
However, with the discovery of the predicted elements, notably gallium in 1875, scandium in 1879, and germanium in 1886, it began to win wide acceptance.
The subsequent proof of many of his predictions within his lifetime brought fame to Mendeleev as the founder of the periodic law.
This organization surpassed earlier attempts at classification by Alexandre-Émile Béguyer de Chancourtois, who published the telluric helix, an early, three-dimensional version of the periodic table of the elements in 1862, John Newlands, who proposed the law of octaves (a precursor to the periodic law) in 1864, and Lothar Meyer, who developed an early version of the periodic table with 28 elements organized by valence in 1864.
Mendeleev's table did not include any of the noble gases, however, which had not yet been discovered.
Gradually the periodic law and table became the framework for a great part of chemical theory.
By the time Mendeleyev died in 1907, he enjoyed international recognition and had received distinctions and awards from many countries.
In 1873, Jacobus Henricus van 't Hoff and Joseph Achille Le Bel, working independently, developed a model of chemical bonding that explained the chirality experiments of Pasteur and provided a physical cause for optical activity in chiral compounds.
van 't Hoff's publication, called V"oorstel tot Uitbreiding der Tegenwoordige in de Scheikunde gebruikte Structuurformules in de Ruimte", etc.
(Proposal for the development of 3-dimensional chemical structural formulae) and consisting of twelve pages text and one page diagrams, gave the impetus to the development of stereochemistry.
The concept of the "asymmetrical carbon atom", dealt with in this publication, supplied an explanation of the occurrence of numerous isomers, inexplicable by means of the then current structural formulae.
At the same time he pointed out the existence of relationship between optical activity and the presence of an asymmetrical carbon atom. 
Professor Dmitri Mendeleev published the first periodic table of the chemical elements in 1869 based on properties which appeared with some regularity as he laid out the elements from lightest to heaviest.
When Mendeleev proposed his periodic table, he noted gaps in the table, and predicted that as-yet-unknown elements existed with properties appropriate to fill those gaps.